{"id":28524,"date":"2022-06-04T16:00:01","date_gmt":"2022-06-04T10:30:01","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=28524"},"modified":"2022-05-23T15:13:41","modified_gmt":"2022-05-23T09:43:41","slug":"ncert-solutions-for-class-10-maths-chapter-8-ex-8-2","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-2\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2"},"content":{"rendered":"

These 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>\n

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.2<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\nEvaluate the following:
\n\"NCERT
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

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\"NCERT<\/p>\n

(ii) We have given,
\n\"NCERT<\/p>\n

(iii) We have given,
\n\"NCERT
\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\"NCERT<\/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

\"NCERT<\/p>\n

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<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"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. 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