NCERT Solutions for Class 10 Maths<\/a> Chapter 8 Introduction to Trigonometry Ex 8.2 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\nNCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.2<\/h2>\n <\/p>\n
Question 1. \nEvaluate the following: \n \nSolution: \n <\/p>\n
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Question 2. \nChoose the correct option and justify your choice: \n(i) \\(\\frac{2 \\tan 30^{\\circ}}{1+\\tan ^{2} 30^{\\circ}}\\) = \n(A) sin 600 (B) cos 60\u00b0 \n(C) tan 60\u00b0 (D) sin 300<\/p>\n
(ii) \\(\\frac{1-\\tan ^{2} 45^{\\circ}}{1+\\tan ^{2} 45^{\\circ}}\\) = \n(A) tan 90\u00b0 (B) 1 \n(C) sin 450 (D) O<\/p>\n
(iii) sin 2A = 2 sin A is true when A = \n(A) 00 (B) 30\u00b0 \n(C) 45\u00b0 (D) 60\u00b0<\/p>\n
(iv) \\(\\frac{2 \\tan 30^{\\circ}}{1-\\tan ^{2} 30^{\\circ}}\\) = \n(A) cos 60\u00b0 (B) cos 60\u00b0 \n(C) tan 60\u00b0 (D) sin 300 \nSolution: \n(i) We have given, \n <\/p>\n
(ii) We have given, \n <\/p>\n
(iii) We have given, \n \nTherefore, \nsin 2 A = 2 sin A is true only when A = 0\u00b0 \n\u2234 correct option is (A)<\/p>\n
(iv) We have given, \n <\/p>\n
Question 3. \nIf tan (A + B) = \u221a3 and tan (A – B) = \\(\\frac { 1 }{ \\surd 3 }\\); 0\u00b0 < A + B \u2264 90\u00b0; A > B, find A and B. \nSolution: \nWe have given \ntan (A + B) = \u221a3 \n\u21d2 tan (A + B) = tan 60\u00b0 \n\u21d2 A + B = 60\u00b0 … (i) \ntan (A – B) = \\(\\frac { 1 }{ \\surd 3 }\\) \n\u21d2 tan (A – B) = tan 30\u00b0 \n\u21d2 A – B = 30\u00b0 … (ii) \nAdding equation (i) and (ii), we get \n2A = 90\u00b0 \u21d2 A = 45\u00b0 \nPutting the velue of A in equation (i), we get \n45\u00b0 + B = 60\u00b0 \u21d2 B = 60\u00b0 – 45\u00b0 = 15\u00b0 \nTherefore A = 45\u00b0 and B = 15\u00b0<\/p>\n
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Question 4. \nState whether the following statements are true or false. Justify your answer. \n(i) sin (A + B) = sin A + sin B. \n(ii) The value of sin \u03b8 increases as \u03b8 increases. \n(iii) The value of cos \u03b8 increases as \u03b8 increases. \n(iv) sin \u03b8 = cos \u03b8 for all values of \u03b8. \n(v) cot A is not defined for A = 0\u00b0. \nSolution: \n(i) False, because if A = 60\u00b0 and B = 30\u00b0 then \nsin (A + B) = sin (60\u00b0 – 30\u00b0) \n= sin 90\u00b0 = 1 \nsin A + sin B = sin 60\u00b0 + sin 30\u00b0 \n= \\(\\frac{\\sqrt{3}}{2}+\\frac{1}{2}\\) = \\(\\frac{\\sqrt{3}+1}{2}\\) \n\u2234 sin (A + B) \u2260 sin A + sin B, when A = 60\u00b0 and B = 30\u00b0<\/p>\n
(ii) True, because the value of sin \u03b8 increases as \u03b8 increases from \u03b8 to 90\u00b0, but when \u03b8 increases from 90\u00b0 to 180\u00b0 then the value of sin 0 decreases.<\/p>\n
(iii) False, because the value of cos \u03b8 decreases as \u03b8 increases from 0 to 90\u00b0.<\/p>\n
(iv) False, because sin \u03b8 = cos \u03b8 is true only when \u03b8 = 45\u00b0. It is not true for all values of \u03b8,<\/p>\n
(iv) True, because cot 0\u00b0 = \\(\\frac { 1 }{ 0 }\\) = not defined.<\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.2 Question 1. Evaluate the following: Solution: Question 2. Choose the correct option and justify your choice: (i) …<\/p>\n
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","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":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[2],"tags":[],"yoast_head":"\nNCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n