{"id":11674,"date":"2022-08-14T01:47:11","date_gmt":"2022-08-13T20:17:11","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11674"},"modified":"2022-08-14T01:47:18","modified_gmt":"2022-08-13T20:17:18","slug":"in-triangle-abc-right-angled-at-b-it-tan-a-1over-sqrt3-find-the-value-of-i-sin-a-cos-c-cos-a-sin-c-ii-cos-a-cos-c-sin-a-sin-c","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/in-triangle-abc-right-angled-at-b-it-tan-a-1over-sqrt3-find-the-value-of-i-sin-a-cos-c-cos-a-sin-c-ii-cos-a-cos-c-sin-a-sin-c\/","title":{"rendered":"In \\(\\triangle\\) ABC right angled at B, it tan A = \\(1\\over \\sqrt{3}\\), find the value of   (i) sin A cos C + cos A sin C            (ii) cos A cos C &#8211; sin A sin C"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Consider a \\(\\triangle\\) ABC, in which \\(\\angle\\) B = 90<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11686 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-9.jpeg?resize=265%2C218&#038;ssl=1\" alt=\"triangle\" width=\"265\" height=\"218\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-9.jpeg?resize=300%2C247&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-9.jpeg?resize=1024%2C843&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-9.jpeg?resize=768%2C632&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-9.jpeg?resize=1536%2C1265&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/08\/trigonometry8-1-9.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 265px) 100vw, 265px\" data-recalc-dims=\"1\" \/><\/p>\n<p>For \\(\\angle\\) A, we have :<\/p>\n<p>Base = AB, Perp. = BC,\u00a0 and\u00a0 \u00a0Hyp. = AC,<\/p>\n<p>tan A = \\(\\perp\\over base\\) = \\(BC\\over AB\\) = \\(1\\over \\sqrt{3}\\)<\/p>\n<p>Let BC = k and AB = \\(\\sqrt{3} k,<\/p>\n<p>AC = \\(\\sqrt{{AB}^2 + {BC}^2}\\) = 2k<\/p>\n<p>\\(\\therefore\\)\u00a0 \u00a0sin A = \\(\\perp\\over hyp.\\) = \\(BC\\over AC\\) = \\(k\\over 2k\\) = \\(1\\over 2\\)<\/p>\n<p>and,\u00a0 cos A = \\(base\\over hyp.\\) = \\(AB\\over AC\\) = \\(\\sqrt{3}k\\over 2k\\) = \\(\\sqrt{3}\\over 2\\)<\/p>\n<p>For \\(\\angle\\) C, we have :<\/p>\n<p>Base = BC, Perp = AB and Hyp. = AC,<\/p>\n<p>\\(\\therefore\\)\u00a0 \u00a0sin C = \\(\\perp\\over hyp.\\) = \\(AB\\over AC\\) = \\(\\sqrt{3}k\\over 2k\\) = \\(\\sqrt{3}\\over 2\\)<\/p>\n<p>and,\u00a0 cos C = \\(base\\over hyp.\\) = \\(BC\\over AC\\) = \\(k\\over 2k\\) = \\(1\\over 2\\)<\/p>\n<p><strong>(i)<\/strong>\u00a0 sin A cos C + cos A sin C = 1<\/p>\n<p><strong>(ii)<\/strong>\u00a0 cos A cos C &#8211; sin A sin C = 0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Consider a \\(\\triangle\\) ABC, in which \\(\\angle\\) B = 90 For \\(\\angle\\) A, we have : Base = AB, Perp. = BC,\u00a0 and\u00a0 \u00a0Hyp. = AC, tan A = \\(\\perp\\over base\\) = \\(BC\\over AB\\) = \\(1\\over \\sqrt{3}\\) Let BC = k and AB = \\(\\sqrt{3} k, AC = \\(\\sqrt{{AB}^2 + {BC}^2}\\) = 2k &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/in-triangle-abc-right-angled-at-b-it-tan-a-1over-sqrt3-find-the-value-of-i-sin-a-cos-c-cos-a-sin-c-ii-cos-a-cos-c-sin-a-sin-c\/\"> <span class=\"screen-reader-text\">In \\(\\triangle\\) ABC right angled at B, it tan A = \\(1\\over \\sqrt{3}\\), find the value of   (i) sin A cos C + cos A sin C            (ii) cos A cos C &#8211; sin A sin C<\/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>In \\(\\triangle\\) ABC right angled at B, it tan A = \\(1\\over \\sqrt{3}\\), find the value of  (i) sin A cos C + cos A sin C      (ii) cos A cos C - sin A sin C - 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\/in-triangle-abc-right-angled-at-b-it-tan-a-1over-sqrt3-find-the-value-of-i-sin-a-cos-c-cos-a-sin-c-ii-cos-a-cos-c-sin-a-sin-c\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In \\(\\triangle\\) ABC right angled at B, it tan A = \\(1\\over \\sqrt{3}\\), find the value of  (i) sin A cos C + cos A sin C      (ii) cos A cos C - sin A sin C - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Consider a (triangle) ABC, in which (angle) B = 90 For (angle) A, we have : Base = AB, Perp. = BC,\u00a0 and\u00a0 \u00a0Hyp. = AC, tan A = (perpover base) = (BCover AB) = (1over sqrt{3}) Let BC = k and AB = (sqrt{3} k, AC = (sqrt{{AB}^2 + {BC}^2}) = 2k &hellip; 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