{"id":367,"date":"2023-07-04T13:41:37","date_gmt":"2023-07-04T13:41:37","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%88%d8%b8%d9%8a%d9%81%d8%a9-%d8%ac%d9%8a%d8%a8-%d8%a7%d9%84%d8%aa%d9%85%d8%a7%d9%85-%d8%a7%d9%84%d8%b2%d8%a7%d8%a6%d8%af%d9%8a\/"},"modified":"2023-07-04T13:41:37","modified_gmt":"2023-07-04T13:41:37","slug":"%d9%88%d8%b8%d9%8a%d9%81%d8%a9-%d8%ac%d9%8a%d8%a8-%d8%a7%d9%84%d8%aa%d9%85%d8%a7%d9%85-%d8%a7%d9%84%d8%b2%d8%a7%d8%a6%d8%af%d9%8a","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%88%d8%b8%d9%8a%d9%81%d8%a9-%d8%ac%d9%8a%d8%a8-%d8%a7%d9%84%d8%aa%d9%85%d8%a7%d9%85-%d8%a7%d9%84%d8%b2%d8%a7%d8%a6%d8%af%d9%8a\/","title":{"rendered":"\u0648\u0638\u064a\u0641\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0647\u0646\u0627 \u0643\u0644 \u0634\u064a\u0621 \u0639\u0646 \u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629: \u0645\u0627 \u0647\u064a \u0635\u064a\u063a\u062a\u0647\u0627\u060c \u0648\u062a\u0645\u062b\u064a\u0644\u0647\u0627 \u0627\u0644\u0631\u0633\u0648\u0645\u064a\u060c \u0648\u062e\u0635\u0627\u0626\u0635\u0647\u0627\u060c \u0648\u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0645\u0639 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u062e\u0631\u0649\u060c \u0648\u0645\u0627 \u0625\u0644\u0649 \u0630\u0644\u0643. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"formula-del-coseno-hiperbolico\"><\/span> \u0635\u064a\u063a\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062f\u0627\u0644\u0629 <strong>\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629<\/strong> \u0647\u064a \u0625\u062d\u062f\u0649 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0642\u0637\u0639\u064a\u0629 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0648\u064a\u062a\u0645 \u062a\u0645\u062b\u064a\u0644\u0647\u0627 \u0628\u0627\u0644\u0631\u0645\u0632 <strong>cosh(x)<\/strong> . \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u064a\u0633\u0627\u0648\u064a \u0645\u062c\u0645\u0648\u0639 e <sup>x<\/sup> \u0632\u0627\u0626\u062f e <sup>-x<\/sup> \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 2.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f667377a7e792f2c9f5f5a7a0ecda4e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)=\\cfrac{e^{x}+e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u064a\u0631\u062a\u0628\u0637 \u0631\u064a\u0627\u0636\u064a\u064b\u0627 \u0628\u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629. \u0648\u0641\u064a \u0627\u0644\u0631\u0627\u0628\u0637 \u0627\u0644\u062a\u0627\u0644\u064a \u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u0627\u0637\u0644\u0627\u0639 \u0639\u0644\u0649 \u062e\u0635\u0627\u0626\u0635 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0648\u0638\u0627\u0626\u0641:<\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u0648\u0638\u064a\u0641\u0629-\u0627\u0644\u0627\u0654\u0633\u064a\u0629\/\">\u062e\u0648\u0627\u0635 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\u0629<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"representacion-grafica-del-coseno-hiperbolico\"><\/span> \u062a\u0645\u062b\u064a\u0644 \u0631\u0633\u0648\u0645\u064a \u0644\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0631\u0633\u0648\u0645\u064a \u0644\u0648\u0638\u064a\u0641\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u064a\u0643\u0648\u0646 \u0641\u064a \u0634\u0643\u0644 \u062f\u0627\u0644\u0629 \u062a\u0631\u0628\u064a\u0639\u064a\u0629 (\u0623\u0648 \u0642\u0637\u0639 \u0645\u0643\u0627\u0641\u0626): <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/cosinus-hyperbolique.webp\" alt=\"\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\" class=\"wp-image-376\" width=\"281\" height=\"308\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u062f\u0627\u0644\u0629-\u0627\u0644\u0642\u0637\u0639-\u0627\u0644\u0645\u0643\u0627\u0641\u064a\u0654-\u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a\/\">\u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a\u0629<\/a><\/span> .<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0631\u0649 \u0628\u0648\u0636\u0648\u062d \u0623\u0646 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0647\u0648 \u062f\u0627\u0644\u0629 \u0632\u0648\u062c\u064a\u0629\u060c \u0644\u0623\u0646\u0647 \u0645\u062a\u0645\u0627\u062b\u0644 \u062d\u0648\u0644 \u0627\u0644\u0645\u062d\u0648\u0631 y.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0641\u0625\u0646 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0644\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u064a\u062e\u062a\u0644\u0641 \u062a\u0645\u0627\u0645\u064b\u0627 \u0639\u0646 \u0631\u0633\u0645 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 (\u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629)\u060c \u0648\u0647\u064a \u062f\u0627\u0644\u0629 \u062f\u0648\u0631\u064a\u0629. \u064a\u0645\u0643\u0646\u0643 \u0645\u0634\u0627\u0647\u062f\u0629 \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0631\u0633\u0648\u0645\u064a \u0644\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0648\u062c\u0645\u064a\u0639 \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0645\u0639 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0641\u064a \u0627\u0644\u0631\u0627\u0628\u0637 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u0648\u0638\u064a\u0641\u0629-\u062c\u064a\u0628-\u0627\u0644\u062a\u0645\u0627\u0645\/\">\u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0631\u0633\u0648\u0645\u064a \u0644\u0648\u0638\u064a\u0641\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"caracteristicas-del-coseno-hiperbolico\"><\/span> \u062e\u0635\u0627\u0626\u0635 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u064a\u062d\u062a\u0631\u0645 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0645\u062c\u0627\u0644 \u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0647\u0648 \u062c\u0645\u064a\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd1539b66edeb38040ed80168e1fd9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0630\u0644\u0643\u060c \u0646\u0637\u0627\u0642 (\u0623\u0648 \u0645\u062f\u0649) \u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0647\u0648 1 \u0648\u0643\u0644 \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0623\u0643\u0628\u0631 \u0645\u0646 1:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60c76341385ea1ebb5f20476cd8226f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Im } f= [1,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0647\u0648 \u0648\u0638\u064a\u0641\u0629 \u0645\u0633\u062a\u0645\u0631\u0629 \u0648\u062d\u062a\u0649.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91f3c4459fc8d8840fd902946c851d1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{cosh}(-x)=\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062a\u062a\u0642\u0627\u0637\u0639 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0639 \u0627\u0644\u0645\u062d\u0648\u0631 Y \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 x=0.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd01415f329053c1a450867378fc1582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u064a\u0633 \u0644\u0647\u0627 \u0646\u0642\u0637\u0629 \u062a\u0642\u0627\u0637\u0639 \u0645\u0639 \u0627\u0644\u0645\u062d\u0648\u0631 X.<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0625\u0646 \u062d\u062f\u064a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 (\u0627\u0644\u0645\u0648\u062c\u0628 \u0648\u0627\u0644\u0633\u0627\u0644\u0628) \u0644\u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u064a\u0639\u0637\u064a\u0627\u0646 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a5aadc0c48684e553e9971aefe442d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to+\\infty}\\text{cosh}(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"161\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fb2a605c43e81635473abf73554d264f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to-\\infty}\\text{cosh}(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"161\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u064a\u062a\u0646\u0627\u0642\u0635 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u062d\u062a\u0649 x = 0 \u0648\u0645\u0646 \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629 \u064a\u0632\u062f\u0627\u062f \u0625\u0644\u0649 \u0623\u062c\u0644 \u063a\u064a\u0631 \u0645\u0633\u0645\u0649\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u062d\u062f \u0623\u062f\u0646\u0649 \u0639\u0646\u062f x = 0.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd01415f329053c1a450867378fc1582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u062d\u062f\u0628\u0629 \u0641\u064a \u0645\u062c\u0627\u0644\u0647\u0627\u060c \u0644\u0630\u0644\u0643 \u0644\u064a\u0633 \u0644\u0647\u0627 \u0646\u0642\u0637\u0629 \u0627\u0646\u0639\u0637\u0627\u0641.<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0645\u0634\u062a\u0642 \u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0647\u0648 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a7a982aae764353843a57652f9a6797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(x) \\ \\longrightarrow \\ f'(x)=\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"286\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062a\u0643\u0627\u0645\u0644 \u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0647\u0648 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a509c96c515bb7115359764e7e4451df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\int \\text{cosh}(x) \\ dx= \\text{senh}(x) + C\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"221\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0643\u062b\u064a\u0631\u0629 \u062d\u062f\u0648\u062f \u062a\u0627\u064a\u0644\u0648\u0631 (\u0623\u0648 \u0633\u0644\u0633\u0644\u0629 \u0645\u0627\u0643\u0644\u0648\u0631\u064a\u0646) \u0644\u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdbe87b63234b62e226371256f8a6c8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)=1+\\cfrac{x^2}{2!}+\\cfrac{x^4}{4!}+\\cfrac{x^6}{6!}+\\dots=\\sum_{n=0}^\\infty\\cfrac{x^{2n}}{(2n)!}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"350\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062a\u062d\u0648\u064a\u0644 \u0644\u0627\u0628\u0644\u0627\u0633 \u0644\u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a: <\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ee373a19450972f0c4cccc3a273770e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathcal{L}\\bigl[\\text{cosh}(at)\\bigr]=\\cfrac{s}{s^2-a^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"171\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"relaciones-matematicas-del-coseno-hiperbolico\"><\/span> \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0644\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0633\u0646\u0631\u0649 \u0643\u064a\u0641 \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0645\u0646 \u062f\u0648\u0627\u0644 \u0632\u0627\u0626\u062f\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u062d\u064a\u062b \u0625\u0646\u0647\u0627 \u0643\u0644\u0647\u0627 \u0645\u0631\u062a\u0628\u0637\u0629 \u0631\u064a\u0627\u0636\u064a\u064b\u0627.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u062a\u0631\u0628\u0637 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0628\u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4317a445a90e4d139b47db7cf4a49a1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}^2(x)-\\text{senh}^2(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong> <a href=\"https:\/\/mathority.org\/ar\/\u062f\u0627\u0644\u0629-\u0627\u0644\u062c\u064a\u0628-\u0627\u0644\u0632\u0627\u064a\u0654\u062f\u064a\u0629\/\"><span style=\"text-decoration: underline;\">\u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0626\u062f\u064a<\/span><\/a><\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u0631\u0628\u0637 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0627\u0644\u062b\u0644\u0627\u062b \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 (\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0648\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0648\u0627\u0644\u0638\u0644) \u0628\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-12f286528bc0635705aadbe510b6ceb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}(x)=\\cfrac{\\text{senh}(x)}{\\text{cosh}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"144\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u064a\u0645\u0643\u0646 \u062a\u062d\u062f\u064a\u062f \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0644\u0644\u062c\u0645\u0639 (\u0623\u0648 \u0627\u0644\u0637\u0631\u062d) \u0644\u0639\u062f\u062f\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u064a\u0646 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-75dff3fbdfd533e08cf581767a0d9b7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(x+y)=\\text{cosh}(x)\\text{cosh}(y)+\\text{senh}(y)\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"363\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3762e67762eecb02ed3d30c39febca9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(x-y)=\\text{cosh}(x)\\text{cosh}(y)-\\text{senh}(y)\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"363\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0644\u0639\u062f\u062f \u0645\u0632\u062f\u0648\u062c \u064a\u0633\u0627\u0648\u064a \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0648\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0644\u0647\u0630\u0627 \u0627\u0644\u0631\u0642\u0645:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-be5e2f8a1f407e6dce0c53932575d545_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(2x)=\\text{cosh}^2(x)+\\text{senh}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"242\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u062c\u0645\u0639 \u0623\u0648 \u0637\u0631\u062d \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02b9d1c798f2639e6503add69dcdb401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)+\\text{cosh}(y)=2\\text{cosh}\\left(\\frac{x+y}{2}\\right)\\text{cosh}\\left(\\frac{x-y}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"384\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ec9d613adc720e383f1c3c0c9c8ca5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)-\\text{cosh}(y)=2\\text{senh}\\left(\\frac{x+y}{2}\\right)\\text{senh}\\left(\\frac{x-y}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"386\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0645\u0631\u0628\u0639 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u0628\u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33c90357c8680ebd2ca5725aad7703f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}^2(x)=\\cfrac{1}{2}\\Bigl(\\text{cosh}(2x)+1\\Bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"215\" style=\"vertical-align: -12px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u062c\u062f \u0647\u0646\u0627 \u0643\u0644 \u0634\u064a\u0621 \u0639\u0646 \u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629: \u0645\u0627 \u0647\u064a \u0635\u064a\u063a\u062a\u0647\u0627\u060c \u0648\u062a\u0645\u062b\u064a\u0644\u0647\u0627 \u0627\u0644\u0631\u0633\u0648\u0645\u064a\u060c \u0648\u062e\u0635\u0627\u0626\u0635\u0647\u0627\u060c \u0648\u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0645\u0639 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u062e\u0631\u0649\u060c \u0648\u0645\u0627 \u0625\u0644\u0649 \u0630\u0644\u0643. \u0635\u064a\u063a\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a \u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629 \u0647\u064a \u0625\u062d\u062f\u0649 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0642\u0637\u0639\u064a\u0629 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