10 Maths NcertSolutions Chapter 8 4 | Trigonometric Functions

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1oth maths solutions
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Triangle Geometry

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Mathematics  (www.tiwariacademy.net) (Class X)   www.tiwariacademy.com A Free web support in education  1 Question 1: Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. Answer 1:  We know that, Question 2: Write all the other trigonometric ratios of ∠ A in terms of sec A. Answer 2:  We know that, Therefore, We know that, However, Therefore, Also,  Mathematics  (www.tiwariacademy.net) (Class X)   www.tiwariacademy.com A Free web support in education  2 Also, sin 2  A + cos 2  A = 1 sin 2   A = 1 − cos 2  A tan 2 A + 1 = sec 2 A tan 2 A = sec 2 A − 1 Question 3: Evaluate (i)   (ii)   sin25° cos65° + cos25° sin65° Answer 3:  (i)  Mathematics  (www.tiwariacademy.net) (Class X)   www.tiwariacademy.com A Free web support in education  3 = 1 (ii) sin25° cos65° + cos25° sin65° = sin 2 25° + cos 2 25° = 1 (As sin 2 A + cos 2 A = 1) Question 4: Choose the correct option. Justify your choice. (i) 9 sec 2   A − 9 tan 2  A = (A)   1 (B) 9 (C) 8 (D) 0 (ii) (1 + tan θ + sec θ) (1 + cot θ − cosec θ) (A) 0 (B)1 (C) 2 (D) −1 (iii) (secA + tanA) (1 − sinA) = (A)   secA (B) sinA (C) cosecA (D) cosA (iv) (A)   sec 2 A (B) − 1 (C) cot 2 A (D) tan 2 A Answer 4:  (i) 9 sec 2 A − 9 tan 2 A = 9 (sec 2 A − tan 2 A) = 9 (1) [As sec 2   A − tan 2  A = 1] = 9 Hence, alternative (B) is correct.  Mathematics  (www.tiwariacademy.net) (Class X)   www.tiwariacademy.com A Free web support in education  4 (ii) (1 + tan θ + sec θ) (1 + cot θ − cosec θ) Hence, alternative (C) is correct. (iii)   (secA + tanA) (1 − sinA) = cosA Hence, alternative (D) is correct. (iv)   Hence, alternative (D) is correct.
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