{"id":11708,"date":"2022-08-15T17:04:48","date_gmt":"2022-08-15T11:34:48","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11708"},"modified":"2022-08-15T17:04:56","modified_gmt":"2022-08-15T11:34:56","slug":"state-whether-the-following-are-true-or-false-justify-you-answer","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/state-whether-the-following-are-true-or-false-justify-you-answer\/","title":{"rendered":"State whether the following are true or false. Justify you answer."},"content":{"rendered":"

Question :<\/h2>\n

(i)<\/strong>\u00a0 Sin (A + B) = sin A + sin B<\/p>\n

(ii)<\/strong>\u00a0 The value of \\(sin \\theta\\) increases as \\(\\theta\\) increases.<\/p>\n

(iii)<\/strong>\u00a0 The value of \\(cos \\theta\\) increases as \\(\\theta\\) increases.<\/p>\n

(iv)<\/strong>\u00a0 \\(sin \\theta\\) = \\(cos \\theta\\) for all values of \\(\\theta\\).<\/p>\n

(v)<\/strong>\u00a0 Cot A is not defined for A = 0.<\/p>\n

Solution :<\/h2>\n

(i)\u00a0 False<\/strong>. Because<\/p>\n

when A = 60 and B = 30. Then,<\/p>\n

sin (A + B) = sin (60 + 30) = sin 90 = 1<\/p>\n

and, sin A + sin B = sin 60 + sin 30\u00a0 = \\(\\sqrt{3} + 1\\over 2\\)<\/p>\n

So, sin (A + B) \\(\\ne\\)\u00a0 sin A + sin B<\/p>\n

(ii)\u00a0 True.<\/strong><\/p>\n

(iii) False<\/strong><\/p>\n

(iv)\u00a0 False<\/strong>. Because it is true for only \\(\\theta\\) = 45<\/p>\n

(v)\u00a0 True<\/strong>. Because tan 0 = 0 and cot 0 = \\(1\\over tan 0\\) = \\(1\\over 0\\) i.e. not defined.<\/p>\n","protected":false},"excerpt":{"rendered":"

Question : (i)\u00a0 Sin (A + B) = sin A + sin B (ii)\u00a0 The value of \\(sin \\theta\\) increases as \\(\\theta\\) increases. (iii)\u00a0 The value of \\(cos \\theta\\) increases as \\(\\theta\\) increases. (iv)\u00a0 \\(sin \\theta\\) = \\(cos \\theta\\) for all values of \\(\\theta\\). (v)\u00a0 Cot A is not defined for A = 0. Solution …<\/p>\n

State whether the following are true or false. Justify you answer.<\/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":"\nState whether the following are true or false. 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