{"id":11969,"date":"2022-09-08T02:16:21","date_gmt":"2022-09-07T20:46:21","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11969"},"modified":"2022-09-08T02:17:10","modified_gmt":"2022-09-07T20:47:10","slug":"choose-the-correct-option-justify-your-choice","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/choose-the-correct-option-justify-your-choice\/","title":{"rendered":"Choose the correct option. Justify your choice :"},"content":{"rendered":"

Question :<\/h2>\n

Choose the correct option. Justify your choice :<\/p>\n

(i)<\/strong>\u00a0 \\(9 sec^2 A – 9 tan^2 A\\) =<\/p>\n

(a)\u00a0 1<\/p>\n

(b)\u00a0 9<\/p>\n

(c)\u00a0 8<\/p>\n

(d)\u00a0 0<\/p>\n

(ii)<\/strong>\u00a0 \\((1 – tan \\theta + sec \\theta)\\)\\((1 + cot \\theta – cosec \\theta)\\) =<\/p>\n

(a)\u00a0 0<\/p>\n

(b)\u00a0 1<\/p>\n

(c)\u00a0 2<\/p>\n

(d) -1<\/p>\n

(iii)<\/strong>\u00a0 (sec A + tan A)(1 – sin A) =<\/p>\n

(a)\u00a0 sec A<\/p>\n

(b)\u00a0 sin A<\/p>\n

(c)\u00a0 cosec A<\/p>\n

(c)\u00a0 cos A<\/p>\n

(iv)<\/strong>\u00a0 \\(1 + tan^2 A\\over 1 + cot^2 A\\) =<\/p>\n

(a)\u00a0 \\(sec^2 A\\)<\/p>\n

(b)\u00a0 -1<\/p>\n

(c)\u00a0 \\(cot^2 A\\)<\/p>\n

(d)\u00a0 \\(tan^2 A\\)<\/p>\n

Solution :<\/h2>\n

(i)\u00a0 (b)\u00a0\u00a0<\/strong>Because : \\(9 sec^2 A – 9 tan^2 A\\) = 9(\\(9 sec^2 A – 9 tan^2 A\\)) =\u00a0 9(1) = 9<\/strong><\/p>\n

(ii)\u00a0 (c)<\/strong>\u00a0 Because : \\((1 – tan \\theta\\) + sec \\theta)\\)\\((1 + cot \\theta – cosec \\theta)\\)<\/p>\n

= (1 + \\(sin\\theta\\over cos\\theta\\) + \\(1\\over cos\\theta\\))(1 + \\(cos\\theta\\over sin\\theta\\) – \\(1\\over sin\\theta\\))<\/p>\n

= \\(({cos\\theta +sin\\theta})^2 – 1\\over cos\\theta sin\\theta \\)<\/p>\n

= \\(1 + 2cos\\theta sin\\theta – 1\\over sin\\theta cos\\theta\\) = \\(2sin\\theta cos\\theta\\over sin\\theta cos\\theta\\) = 2<\/strong><\/p>\n

(iii)\u00a0 (d)<\/strong>\u00a0 Because<\/p>\n

(sec A + tan A)(1 – sin A) = (\\(1\\over cos A\\) + \\(sin A\\over cos A\\))(1 – sin A) = (\\(1 + sin A\\over cos A\\))(1 – sin A)<\/p>\n

= \\(1 – sin^2A\\over cos A\\) = \\(cos^2 A\\over cos A\\) = cos A<\/strong><\/p>\n

(iv)\u00a0 (d)<\/strong>\u00a0 Because<\/p>\n

\\(1 + tan^2 A\\over 1 + cot^2 A\\) = \\(1 + tan^2 A\\over 1 + {1\\over tan^2 A}\\) = (\\(1 + tan^2 A\\)) \\(\\times\\) \\(tan^2 A\\over 1 + tan^2 A\\) = \\(tan^2 A\\)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Choose the correct option. Justify your choice : (i)\u00a0 \\(9 sec^2 A – 9 tan^2 A\\) = (a)\u00a0 1 (b)\u00a0 9 (c)\u00a0 8 (d)\u00a0 0 (ii)\u00a0 \\((1 – tan \\theta + sec \\theta)\\)\\((1 + cot \\theta – cosec \\theta)\\) = (a)\u00a0 0 (b)\u00a0 1 (c)\u00a0 2 (d) -1 (iii)\u00a0 (sec A + tan …<\/p>\n

Choose the correct option. Justify your choice :<\/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":"\nChoose the correct option. 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