{"id":11714,"date":"2022-08-16T00:58:05","date_gmt":"2022-08-15T19:28:05","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11714"},"modified":"2022-08-16T00:58:12","modified_gmt":"2022-08-15T19:28:12","slug":"show-that-i-tan-48-tan-23-tan-42-tan-67-1-ii-cos-38-cos-52-sin-38-sin-52-0","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/show-that-i-tan-48-tan-23-tan-42-tan-67-1-ii-cos-38-cos-52-sin-38-sin-52-0\/","title":{"rendered":"Show that :  (i) tan 48 tan 23 tan 42 tan 67 = 1    (ii)  cos 38 cos 52 &#8211; sin 38 sin 52 = 0"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p><strong>(i)<\/strong>\u00a0 L.H.S = tan 48 tan 23 tan 42 tan 67 = \\(1\\over cot 48\\). tan 23 tan 42 \\(1\\over cot 67\\)<\/p>\n<p>= \\(1\\over cot (90 &#8211; 42)\\). tan 23 tan 42 \\(1\\over cot (90 &#8211; 23)\\) = \\(1\\over tan 42\\). tan 23 tan 42 \\(1\\over tan 23\\)<\/p>\n<p>= <strong>1 = R.H.S.<\/strong><\/p>\n<p><strong>(ii)<\/strong>\u00a0 L.H.S = cos 38 cos 52 &#8211; sin 38 sin 52 = cos 38.cos(90 &#8211; 38) &#8211; sin 38 sin(90 &#8211; 38)<\/p>\n<p>= cos 38 sin 38 &#8211; sin 38 cos 38 = <strong>0 = R.H.S.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : (i)\u00a0 L.H.S = tan 48 tan 23 tan 42 tan 67 = \\(1\\over cot 48\\). tan 23 tan 42 \\(1\\over cot 67\\) = \\(1\\over cot (90 &#8211; 42)\\). tan 23 tan 42 \\(1\\over cot (90 &#8211; 23)\\) = \\(1\\over tan 42\\). tan 23 tan 42 \\(1\\over tan 23\\) = 1 = R.H.S. (ii)\u00a0 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/show-that-i-tan-48-tan-23-tan-42-tan-67-1-ii-cos-38-cos-52-sin-38-sin-52-0\/\"> <span class=\"screen-reader-text\">Show that :  (i) tan 48 tan 23 tan 42 tan 67 = 1    (ii)  cos 38 cos 52 &#8211; sin 38 sin 52 = 0<\/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>Show that : (i) tan 48 tan 23 tan 42 tan 67 = 1  (ii) cos 38 cos 52 - sin 38 sin 52 = 0 - 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\/show-that-i-tan-48-tan-23-tan-42-tan-67-1-ii-cos-38-cos-52-sin-38-sin-52-0\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Show that : (i) tan 48 tan 23 tan 42 tan 67 = 1  (ii) cos 38 cos 52 - sin 38 sin 52 = 0 - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : (i)\u00a0 L.H.S = tan 48 tan 23 tan 42 tan 67 = (1over cot 48). tan 23 tan 42 (1over cot 67) = (1over cot (90 &#8211; 42)). tan 23 tan 42 (1over cot (90 &#8211; 23)) = (1over tan 42). tan 23 tan 42 (1over tan 23) = 1 = R.H.S. 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