{"id":165533,"date":"2024-03-27T15:27:23","date_gmt":"2024-03-27T09:57:23","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=165533"},"modified":"2024-03-27T15:27:24","modified_gmt":"2024-03-27T09:57:24","slug":"if-cos-%ce%b8-sin-%ce%b8-%e2%88%9a2-cos-%ce%b8-find-the-value-of-cos-%ce%b8-sin-%ce%b8","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/if-cos-%ce%b8-sin-%ce%b8-%e2%88%9a2-cos-%ce%b8-find-the-value-of-cos-%ce%b8-sin-%ce%b8\/","title":{"rendered":"If Cos \u03b8+ Sin \u03b8\u00a0= \u221a2 Cos \u03b8, find the value of (cos \u03b8 &#8211; sin \u03b8)"},"content":{"rendered":"\n<p> <p class=\"MsoNormal\">If Cos <span style=\"font-family: Arial, sans-serif; color: rgb(71, 71, 71); background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;\">\u03b8+ Sin \u03b8\u00a0<\/span>= \u221a2 Cos \u03b8, find the value of (cos \u03b8 &#8211; sin \u03b8)<\/p> <p class=\"MsoNormal\">Sol:<\/p> <p class=\"MsoNormal\">Shortcut Trick Formula Used:\u00a0\u00a0 cos\u00a0\u03b8 + sin\u00a0\u03b8\u00a0= x, then cos\u00a0\u03b8 &#8211; sin\u00a0\u03b8 =\u00a0\u221a(2 &#8211; x2) <\/p> <p class=\"MsoNormal\">\u00a0Calculation:\u00a0 <\/p> <p class=\"MsoNormal\">Using the above formula, we get\u00a0 <\/p> <p class=\"MsoNormal\"><span style=\"font-family:&quot;Cambria Math&quot;,serif;mso-bidi-font-family:\n&quot;Cambria Math&quot;\">\u21d2<\/span>\u00a0cos\u00a0\u03b8 &#8211;\u00a0sin\u00a0\u03b8\u00a0=\u00a0\u221a{2 &#8211; (\u221a2 cos \u03b8)2}\u00a0\u00a0 <\/p> <p class=\"MsoNormal\">\u00a0<span style=\"font-family:&quot;Cambria Math&quot;,serif;mso-bidi-font-family:&quot;Cambria Math&quot;\">\u21d2<\/span>\u00a0cos\u00a0\u03b8 &#8211;\u00a0sin\u00a0\u03b8\u00a0=\u00a0\u221a{2 &#8211; 2cos2\u00a0\u03b8} <\/p> <p class=\"MsoNormal\">\u00a0<span style=\"font-family:&quot;Cambria Math&quot;,serif;mso-bidi-font-family:&quot;Cambria Math&quot;\">\u21d2<\/span>\u00a0cos\u00a0\u03b8 &#8211;\u00a0sin\u00a0\u03b8\u00a0=\u00a0\u221a2 (1 &#8211; cos2\u03b8) <\/p> <p class=\"MsoNormal\">\u00a0<span style=\"font-family:&quot;Cambria Math&quot;,serif;mso-bidi-font-family:&quot;Cambria Math&quot;\">\u21d2<\/span>\u00a0cos\u00a0\u03b8 &#8211;\u00a0sin\u00a0\u03b8\u00a0=\u00a0\u221a2 sin\u00a0\u03b8\u00a0 <\/p> <\/p>\n","protected":false},"excerpt":{"rendered":"<p>If Cos \u03b8+ Sin \u03b8\u00a0= \u221a2 Cos \u03b8, find the value of (cos \u03b8 &#8211; sin \u03b8) Sol: Shortcut Trick Formula Used:\u00a0\u00a0 cos\u00a0\u03b8 + sin\u00a0\u03b8\u00a0= x, then cos\u00a0\u03b8 &#8211; sin\u00a0\u03b8 =\u00a0\u221a(2 &#8211; x2) \u00a0Calculation:\u00a0 Using the above formula, we get\u00a0 \u21d2\u00a0cos\u00a0\u03b8 &#8211;\u00a0sin\u00a0\u03b8\u00a0=\u00a0\u221a{2 &#8211; (\u221a2 cos \u03b8)2}\u00a0\u00a0 \u00a0\u21d2\u00a0cos\u00a0\u03b8 &#8211;\u00a0sin\u00a0\u03b8\u00a0=\u00a0\u221a{2 &#8211; 2cos2\u00a0\u03b8} \u00a0\u21d2\u00a0cos\u00a0\u03b8 &#8211;\u00a0sin\u00a0\u03b8\u00a0=\u00a0\u221a2 (1 &#8211; cos2\u03b8) [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":165534,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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