NCERT Solutions for Class 10 Maths<\/a> Chapter 8 Introduction to Trigonometry Ex 8.4 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\nNCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.4<\/h2>\n <\/p>\n
Question 1. \nExpress the trigonometric ratios sin A, sec A and tan A in terms of cot A. \nSolution: \nWe know that \n <\/p>\n
Question 2. \nWrite all the other trigonometric ratios of \u2220A in terms of sec A. \nSolution: \nWe know that \n <\/p>\n
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Question 3. \nEvaluate: \n(i) \\(\\frac{\\sin ^{2} 63^{\\circ}+\\sin ^{2} 27^{\\circ}}{\\cos ^{2} 17^{\\circ}+\\cos ^{2} 73^{\\circ}}\\) \n(ii) sin 25\u00b0 cos 65\u00b0 + cos 25\u00b0 sin 65\u00b0 \nSolution: \n(i) We know that \n <\/p>\n
(ii) We know that \nsin 25\u00b0 cos 65\u00b0 + cos 25\u00b0 sin 65\u00b0 \n= sin 25\u00b0 cos (90\u00b0 – 25\u00b0) + cos 25\u00b0 sin (90\u00b0 – 25\u00b0) \n= sin 25\u00b0 sin 25\u00b0 + cos 25\u00b0 cos 25\u00b0 \n= sin\u00b2 25\u00b0 + cos\u00b2 25\u00b0 = 1 (sin\u00b2 \u03b8 + cos\u00b2 \u03b8)<\/p>\n
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Question 4. \nChoose the correct option. Justify your choice. \n(i) 9 sec\u00b2 A – 9 tan\u00b2 A = \n(A) 1 \n(B) 9 \n(C) 8 \n(D) 0<\/p>\n
(ii) (1 + tan \u03b8 + sec \u03b8) (1 + cot \u03b8 – cosec \u03b8 ) = \n(A) 0 \n(B) 1 \n(C) 2 \n(D) -1<\/p>\n
(iii) (sec A + tan A) (1 – sin A) = \n(A) sec A \n(B) sin A \n(C) cosec A \n(D) cos A<\/p>\n
(iv) \\(\\frac{1+\\tan ^{2} A}{1+\\cot ^{2} A}\\) \n(A) sec\u00b2 A \n(B) -1 \n(C) cot\u00b2 A \n(D) tan\u00b2 A \nSolution: \n(i) We know that \n9 sec\u00b2 A – 9 tan\u00b2 A = 9(sec\u00b2 A – tan\u00b2 A) \n= 9 x 1 = 9 \nCorrect option is (B)<\/p>\n
(ii) We know that \n(1 + tan \u03b8 + sec \u03b8) (1 + cot \u03b8 – cosec \u03b8 ) \n \nSo, the correct option is (C)<\/p>\n
(iii) We have given, \n \nSo, the correct option is (D)<\/p>\n
(iv) We have given, \n \nSo, the correct option is (D)<\/p>\n
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Question 5. \nProve the following identities, where the angles involved are acute angles for which the expressions are defined. \n \nSolution: \n \n <\/p>\n
(vi) L.H.S \n\\(\\sqrt{\\frac{1+\\sin A}{1-\\sin A}}\\) \nMultiply both numerator and denominator by \\(\\sqrt{1+\\sin A}\\) \n <\/p>\n
(viii) (sin A + cosec A)\u00b2 + (cos A + sec A)\u00b2 = 7 + tan\u00b2A + cot\u00b2A. \nSolution: \nL.H.S. \n(sin A + cosec A)\u00b2 (cos A + sec A)\u00b2 \n= (sin\u00b2 A + cosec\u00b2 A + 2sin A + cosec A) + (cos\u00b2A + sec\u00b2 A + 2cos. A sec A) \n= sin\u00b2 A + cosec\u00b2 A + \u00b2) + (cos\u00b2 A + sec\u00b2 A + 2) [\u2235sin A cosec A = 1 and cos A sec A = 1] \n= (sin\u00b2 A + cos\u00b2 A) + 4 + sec\u00b2 A + cosec\u00b2 A \n= 5 (1 + tan\u00b2 A) + 1 + cot\u00b2 A) [\u2235 sec\u00b2 A = (1 + tan\u00b2 A) and cosec\u00b2 A = (1 + cot\u00b2 A)] \n= 7 tan\u00b2 A + cot\u00b2 A = R.H.S.<\/p>\n
(ix) (cosec A – sin A) (sec A – cos A) = \\(\\frac{1}{\\tan A+\\cot A}\\) \n[Hint: Simplify LHS and RHS separately] \nSolution: \nL.H.S. \n <\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.4 Question 1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot …<\/p>\n
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4<\/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 8.4 - 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