{"id":11669,"date":"2022-08-14T01:36:56","date_gmt":"2022-08-13T20:06:56","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11669"},"modified":"2022-08-14T01:37:02","modified_gmt":"2022-08-13T20:07:02","slug":"if-cot-theta-7over-8-evaluate-i-1-sintheta1-sinthetaover-1-costheta1-costheta-ii-cot2-theta","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-cot-theta-7over-8-evaluate-i-1-sintheta1-sinthetaover-1-costheta1-costheta-ii-cot2-theta\/","title":{"rendered":"If cot \\(\\theta\\) = \\(7\\over 8\\), evaluate : (i) \\({(1 + sin\\theta)(1 &#8211; sin\\theta)}\\over {(1 + cos\\theta)(1 &#8211; cos\\theta)}\\)       (ii)  \\(cot^2 \\theta\\)"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p><strong>(i)<\/strong>\u00a0 In \\(\\triangle\\) ABC,\u00a0 \\(cot \\theta\\) = \\(7\\over 8\\) = \\(AB\\over BC\\)<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11681 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-7.jpeg?resize=182%2C263&#038;ssl=1\" alt=\"triangles\" width=\"182\" height=\"263\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-7.jpeg?resize=208%2C300&amp;ssl=1 208w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-7.jpeg?resize=711%2C1024&amp;ssl=1 711w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-7.jpeg?resize=768%2C1106&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-7.jpeg?resize=1066%2C1536&amp;ssl=1 1066w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-7.jpeg?resize=1421%2C2048&amp;ssl=1 1421w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-7.jpeg?w=1527&amp;ssl=1 1527w\" sizes=\"(max-width: 182px) 100vw, 182px\" data-recalc-dims=\"1\" \/><\/p>\n<p>Let AB = 7k and BC = 8k<\/p>\n<p>Now, AC = \\(\\sqrt{{AB}^2 + {BC}^2}\\) = \\(\\sqrt{113k^2}\\)<\/p>\n<p>So, AC = \\(\\sqrt{113}k\\)<\/p>\n<p>Thus,\u00a0 \\(sin \\theta\\) = \\(8k\\over \\sqrt{113}k\\) = \\(8\\over \\sqrt{113}\\)<\/p>\n<p>\\(cos \\theta\\) = \\(7k\\over \\sqrt{113}k\\) = \\(7\\over \\sqrt{113}\\)<\/p>\n<p>Now,\u00a0 \\({(1 + sin\\theta)(1 &#8211; sin\\theta)}\\over {(1 + cos\\theta)(1 &#8211; cos\\theta)}\\) = <strong>\\(49\\over 64\\)<\/strong><\/p>\n<p><strong>(ii)<\/strong>\u00a0 \\(cot^2 \\theta\\) = \\(({7\\over 8})^2\\) = <strong>\\(49\\over 64\\)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : (i)\u00a0 In \\(\\triangle\\) ABC,\u00a0 \\(cot \\theta\\) = \\(7\\over 8\\) = \\(AB\\over BC\\) Let AB = 7k and BC = 8k Now, AC = \\(\\sqrt{{AB}^2 + {BC}^2}\\) = \\(\\sqrt{113k^2}\\) So, AC = \\(\\sqrt{113}k\\) Thus,\u00a0 \\(sin \\theta\\) = \\(8k\\over \\sqrt{113}k\\) = \\(8\\over \\sqrt{113}\\) \\(cos \\theta\\) = \\(7k\\over \\sqrt{113}k\\) = \\(7\\over \\sqrt{113}\\) Now,\u00a0 \\({(1 + sin\\theta)(1 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/if-cot-theta-7over-8-evaluate-i-1-sintheta1-sinthetaover-1-costheta1-costheta-ii-cot2-theta\/\"> <span class=\"screen-reader-text\">If cot \\(\\theta\\) = \\(7\\over 8\\), evaluate : (i) \\({(1 + sin\\theta)(1 &#8211; sin\\theta)}\\over {(1 + cos\\theta)(1 &#8211; cos\\theta)}\\)       (ii)  \\(cot^2 \\theta\\)<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,60],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If cot \\(\\theta\\) = \\(7\\over 8\\), evaluate : (i) \\({(1 + sin\\theta)(1 - sin\\theta)}\\over {(1 + cos\\theta)(1 - cos\\theta)}\\)    (ii) \\(cot^2 \\theta\\) - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/if-cot-theta-7over-8-evaluate-i-1-sintheta1-sinthetaover-1-costheta1-costheta-ii-cot2-theta\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If cot \\(\\theta\\) = \\(7\\over 8\\), evaluate : (i) \\({(1 + sin\\theta)(1 - sin\\theta)}\\over {(1 + cos\\theta)(1 - cos\\theta)}\\)    (ii) \\(cot^2 \\theta\\) - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : (i)\u00a0 In (triangle) ABC,\u00a0 (cot theta) = (7over 8) = (ABover BC) Let AB = 7k and BC = 8k Now, AC = (sqrt{{AB}^2 + {BC}^2}) = (sqrt{113k^2}) So, AC = (sqrt{113}k) Thus,\u00a0 (sin theta) = (8kover sqrt{113}k) = (8over sqrt{113}) (cos theta) = (7kover sqrt{113}k) = (7over sqrt{113}) Now,\u00a0 ({(1 + sintheta)(1 &hellip; If cot (theta) = (7over 8), evaluate : (i) ({(1 + sintheta)(1 &#8211; sintheta)}over {(1 + costheta)(1 &#8211; costheta)})    (ii) (cot^2 theta) Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/if-cot-theta-7over-8-evaluate-i-1-sintheta1-sinthetaover-1-costheta1-costheta-ii-cot2-theta\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-08-13T20:06:56+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-08-13T20:07:02+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-7-208x300.jpeg\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/if-cot-theta-7over-8-evaluate-i-1-sintheta1-sinthetaover-1-costheta1-costheta-ii-cot2-theta\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/if-cot-theta-7over-8-evaluate-i-1-sintheta1-sinthetaover-1-costheta1-costheta-ii-cot2-theta\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"If cot \\\\(\\\\theta\\\\) = \\\\(7\\\\over 8\\\\), evaluate : (i) \\\\({(1 + sin\\\\theta)(1 &#8211; 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If cot (theta) = (7over 8), evaluate : (i) ({(1 + sintheta)(1 &#8211; sintheta)}over {(1 + costheta)(1 &#8211; costheta)})    (ii) (cot^2 theta) Read More &raquo;","og_url":"https:\/\/mathemerize.com\/if-cot-theta-7over-8-evaluate-i-1-sintheta1-sinthetaover-1-costheta1-costheta-ii-cot2-theta\/","og_site_name":"Mathemerize","article_published_time":"2022-08-13T20:06:56+00:00","article_modified_time":"2022-08-13T20:07:02+00:00","og_image":[{"url":"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-7-208x300.jpeg"}],"author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/if-cot-theta-7over-8-evaluate-i-1-sintheta1-sinthetaover-1-costheta1-costheta-ii-cot2-theta\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/if-cot-theta-7over-8-evaluate-i-1-sintheta1-sinthetaover-1-costheta1-costheta-ii-cot2-theta\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"If cot \\(\\theta\\) = \\(7\\over 8\\), evaluate : (i) \\({(1 + sin\\theta)(1 &#8211; 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