NCERT Solutions for Class 10 Maths<\/a> Chapter 8 Introduction to Trigonometry Ex 8.3 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\nNCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.3<\/h2>\n <\/p>\n
Question 1. \n(i) \\(\\frac{\\sin 18^{\\circ}}{\\cos 72^{\\circ}}\\) \n(ii) \\(\\frac{\\tan 26^{\\circ}}{\\cot 64^{\\circ}}\\) \n(iii) cos 48\u00b0 – sin 42\u00b0 \n(iv) cosec 31\u00b0 – sec 59\u00b0 \nSolution: \n <\/p>\n
Question 2. \nShow that: \n(i) tan 48\u00b0 tan 23\u00b0 tan 42\u00b0 tan 67\u00b0 = 1 \n(ii) cos 38\u00b0 cos 52\u00b0 – sin 38\u00b0 sin 52\u00b0 = 0 \nSolution: \n(i) LHS = tan 48\u00b0 tan 23\u00b0 tan 42\u00b0 tan 67\u00b0 \n= tan 48\u00b0 tan 23\u00b0 tan (90\u00b0 – 48\u00b0) tan (90\u00b0 – 23\u00b0) \n= tan 48\u00b0 tan 23\u00b0 cot 48\u00b0 cot 23\u00b0 = tan 48\u00b0 tan 23\u00b0 .\\(\\frac{1}{\\tan 48^{\\circ}} \\cdot \\frac{1}{\\tan 23^{\\circ}}\\) \n= 1 = RHS [Verified]<\/p>\n
(ii) LHS = cos 38\u00b0 cos 52\u00b0 – sin 38\u00b0 sin 52\u00b0 \n= cos 38\u00b0 cos (90\u00b0 – 38\u00b0) – sin 38\u00b0 sin (90\u00b0 – 38\u00b0) \n= cos 38\u00b0 sin 38\u00b0- sin 38\u00b0 cos 38\u00b0 = 0 = RHS [Verified]<\/p>\n
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Question 3. \nIf tan 2A = cot (A – 18\u00b0), where 2A is an acute angle, find the value of A. \nSolution: \ntan 2A = cot (A – 18\u00b0) \n\u21d2 cot (90\u00b0 – 2A) = cot (A – 18\u00b0) [\u2235cot (90\u00b0 – \u03b8) = tan \u03b8] \n\u21d2 90\u00b0 – 2A = A – 18\u00b0 \u21d2 3A = 108\u00b0 \u21d2 A = \\(\\frac { 108\u00b0 }{ 3 }\\) \n\u2234 \u2220 A = 36\u00b0<\/p>\n
Question 4. \nIf tan A = cot B, prove that A + B = 90\u00b0. \nSolution: \ntan A = cot B \u21d2 tan A = tan (90\u00b0 – B) [ \u2235 tan (90\u00b0 – \u03b8) = cot \u03b8] \n\u21d2 A = 90\u00b0 – B \u21d2 A + B = 90\u00b0 Proved<\/p>\n
Question 5. \nIf sec 4A = cosec (A – 20\u00b0), where 4A is an acute angle, find the value of A. \nSolution: \nsec 4A = cosec (A – 20\u00b0) \n\u21d2 cosec (90\u00b0 – 4A) = cosec (A – 20\u00b0) [cosec (90\u00b0 – \u03b8) = sec \u03b8] \n\u21d2 90\u00b0 – 4A = A – 20\u00b0 \u21d2 5A = 110\u00b0 \nA = \\(\\frac { 110\u00b0 }{ 5 }\\) \nA = 22\u00b0 \n\u2234 \u2220 A = 22\u00b0<\/p>\n
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Question 6. \nIf A, Band Care interior angles of a triangle ABC, then show that: sin (\\(\\frac { B+C }{ 2 }\\)) = cos \\(\\frac { A }{ 2 }\\) \nSolution: \nWe have given that, \nA, B and C are the interior angles of a triangle ABC \n <\/p>\n
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Question 7. \nExpress sin 61\u00b0 + cos 75\u00b0 in terms of trigonometric ratios of angles between 0\u00b0 and 45\u00b0. \nSolution: \nsin 67\u00b0 + cos 75\u00b0 \nor sin (90\u00b0 – 23\u00b0) + cos (90\u00b0 – 15\u00b0) \nor cos 23\u00b0 + sin 15\u00b0 (\u2235 sin (90\u00b0 – \u03b8) = cos \u03b8 \nand cos (90\u00b0 – \u03b8) = sin \u03b8) \nNow, sin 67\u00b0 + cos 75\u00b0 in term if trigonometric ratios of angles between 0\u00b0 and 45\u00b0. \n(cos 90\u00b0 – 67\u00b0) + (sin 90\u00b0 – 75\u00b0) \n= cos 23\u00b0 + sin 15\u00b0<\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.3 Question 1. (i) (ii) (iii) cos 48\u00b0 – sin 42\u00b0 (iv) cosec 31\u00b0 – sec 59\u00b0 Solution: …<\/p>\n
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3<\/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 8.3 - 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