{"id":11696,"date":"2022-08-14T23:29:21","date_gmt":"2022-08-14T17:59:21","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11696"},"modified":"2022-08-14T23:29:29","modified_gmt":"2022-08-14T17:59:29","slug":"evaluate","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/evaluate\/","title":{"rendered":"Evaluate :"},"content":{"rendered":"

Question :<\/h2>\n

(i)<\/strong>\u00a0 sin 60 cos 30 + cos 60 sin 30<\/p>\n

(ii)<\/strong>\u00a0 \\(2 tan^2 45\\) + \\(cos^2 30\\) – \\(sin^2 60\\)<\/p>\n

(iii)<\/strong>\u00a0 \\(cos 45\\over sec 30 + cosec 30\\)<\/p>\n

(iv)<\/strong>\u00a0 \\(sin 30 + tan 45 – cosec 60\\over sec 30 + cos 60 + cot 45\\)<\/p>\n

(v)<\/strong>\u00a0 \\(5 cos^2 60 + 4 sec^2 30 – tan^2 45\\over sin^2 30 + cos^2 30\\)<\/p>\n

Solution :<\/h2>\n

(i)<\/strong>\u00a0 sin 60 cos 30 + cos 60 sin 30<\/p>\n

On substituting the values of various t-ratios in (1), we get<\/p>\n

Given expression = \\(\\sqrt{3}\\over 2\\) \\(\\times\\) \\(\\sqrt{3}\\over 2\\) + \\(1\\over 2\\) \\(\\times\\) \\(1\\over 2\\) = \\(4\\over 4\\) = 1<\/strong><\/p>\n

(ii)<\/strong>\u00a0 \\(2 tan^2 45\\) + \\(cos^2 30\\) – \\(sin^2 60\\) = 2 \\(\\times\\) \\((1)^2\\) + \\(({\\sqrt{3}\\over 2})^2\\) – \\(({\\sqrt{3}\\over 2})^2\\) = 2<\/strong><\/p>\n

(iii)<\/strong>\u00a0 \\(cos 45\\over sec 30 + cosec 30\\) = \\({1\\over \\sqrt{2}}\\over {2\\over \\sqrt{3}} + 2\\) = \\(1\\over \\sqrt{2}\\) \\(\\times\\) \\(\\sqrt{3}\\over 2 + 2\\sqrt{3}\\)<\/p>\n

= \\(\\sqrt{3}\\over \\sqrt{2} \\times 2(\\sqrt{3} + 1)\\) \\(\\times\\) \\(\\sqrt{3} – 1\\over \\sqrt{3} – 1\\)<\/p>\n

= \\(3 – \\sqrt{3}\\over 4\\sqrt{2}\\).<\/strong><\/p>\n

(iv)<\/strong>\u00a0 \\(sin 30 + tan 45 – cosec 60\\over sec 30 + cos 60 + cot 45\\) = \\({1\\over 2} + 1 – {2\\over \\sqrt{3}}\\over {2\\over \\sqrt{3}} + {1\\over 2} + 1\\)<\/p>\n

= \\(3\\sqrt{3} – 4\\over 3\\sqrt{3} + 4\\)<\/strong><\/p>\n

(v)<\/strong>\u00a0 \\(5 cos^2 60 + 4 sec^2 30 – tan^2 45\\over sin^2 30 + cos^2 30\\) = \\({5\\over 4} + {16\\over 3} – 1\\over {1\\over 4} + {3\\over 4}\\)<\/p>\n

= \\({67\\over 12}\\over {4\\over 4}\\) = \\(67\\over 12\\)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Question : (i)\u00a0 sin 60 cos 30 + cos 60 sin 30 (ii)\u00a0 \\(2 tan^2 45\\) + \\(cos^2 30\\) – \\(sin^2 60\\) (iii)\u00a0 \\(cos 45\\over sec 30 + cosec 30\\) (iv)\u00a0 \\(sin 30 + tan 45 – cosec 60\\over sec 30 + cos 60 + cot 45\\) (v)\u00a0 \\(5 cos^2 60 + 4 sec^2 30 …<\/p>\n

Evaluate :<\/span> Read More »<\/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":"\nEvaluate : - 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\/evaluate\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Evaluate : - 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