NCERT class 10 maths chapter 8 Introduction To Trigonometry
Question 1:Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
Exercise 8.4 maths class 10 Chapter 8 Introduction To Trigonometry
Question 2:Write all the other trigonometric ratios of Ð A in terms of sec A.
CBSE class 10 maths ncert solutions Chapter 8
Question 3:Evaluate : (i) 2 2 2 2 sin 63 sin 27 cos 17 cos 73 °+ ° ° + ° (ii) sin 25° cos 65° + cos 25° sin 65°
class 10 maths solutions Introduction To Trigonometry
Question 4:Choose the correct option. Justify your choice. (i) 9 sec2 A – 9 tan2 A = (A) 1 (B) 9 (C) 8 (D) 0 (ii) (1 + tan q + sec q) (1 + cot q – cosec q) = (A) 0 (B) 1 (C) 2 (D) –1 (iii) (sec A + tan A) (1 – sin A) = (A) sec A (B) sin A (C) cosec A (D) cos A (iv) 2 2 1 tan A 1 + cot A + = (A) sec2 A (B) –1 (C) cot2 A (D) tan2 A
Question 5:Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (i) (cosec q – cot q)2 = 1 cos 1 cos − q + q (ii) cos A 1 sin A 2 sec A 1 + sin A cos A (iii) tan cot 1 sec cosec 1 cot 1 tan q q + = + q q − q − q [Hint : Write the expression in terms of sin q and cos q] (iv) 2 1 sec A sin A sec A 1 – cos A + = [Hint : Simplify LHS and RHS separately] (v) cos A – sin A + 1 cosec A + cot A, cos A + sin A – 1 = using the identity cosec2 A = 1 + cot2 A. (vi) 1 sinA sec A + tan A 1 – sin A + = (vii) 3 3 sin 2 sin tan 2 cos cos q − q = q q − q (viii) (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A (ix) 1 (cosec A – sin A) (sec A – cos A) tanA + cot A = [Hint : Simplify LHS and RHS separately] (x) 2 2 2 1 tan A 1 tan A 1 + cot A 1 – cot A + − = = tan2 A