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If 3 Sin A 5 Cos A 5 Then The Value Of 3 Cos A 5 Sin A 2 Is

1) 4 2) 5 3) 2 4) 9 Answer: (4) 9 Solution: Given, 3 sin A + 5 cos A = 5....(i) Let 3 cos A - 5 sin A = x....(ii) Squaring and... View Article

1) √2 2) 1/√2 3) 0 4) 1 Answer: (3) 0 Solution: Given, A = 5π/4 cos A - sin A = cos 5π/4 - sin 5π/4 = cos(π + π/4) - sin(π +... View Article

1) sin B 2) sin 2B 3) sin 3B 4) None of these Answer: (2) sin 2B Solution: Given, tan A = 1/2, tan B = 1/3 cos 2A = (1 -... View Article

1) -1 2) -2 3) -3 4) -4 Answer: (1) -1 Solution: tan( - 945°) = tan(- 3 × 360° + 135°) = tan(135°) = tan(180° - 45°) = -tan 45° = -1... View Article

1) 1 2) -1 3) 0 4) 2 Answer: (4) 2 Solution: sin²(π/8) + sin²(3π/8) + sin²(5π/8) + sin²(7π/8) = sin²(π/8) + sin²(3π/8) + sin²(π/2... View Article

1) sec A 2) 2 sec A 3) 0 4) 2 Answer: (3) 0 Solution: (sec A + tan A - 1)(sec A - tan A + 1) - 2 tan A = [sec A + (tan A - 1)]... View Article

1) 1 2) 0 3) 1/√2 4) None of these Answer: (4) None of these Solution: We know that, sin(π/2 + θ) = cos θ cos(π/2 - θ) = sin θ... View Article

1) 0 2) 2 tan A 3) 2 cot A 4) 2(tan A - cot A) Answer: (1) 0 Solution: We know that, cot(180° + x) = cot x (quadrant III) cot(90°... View Article

1) -1 2) 0 3) 1 4) ∞ Answer: (3) 1 Solution: cot(45° + θ) cot(45° - θ) = [(cot 45 cot θ - 1)/ (cot 45 + cot θ)] [(cot 45 cot θ +... View Article

1) 1 2) -1 3) sin θ 4) -sin θ Answer: (2) -1 Solution: sin(π + θ) sin(π - θ) cosec2θ = (-sin θ)(sin θ) cosec2θ = -sin2θ cosec2θ... View Article

1) 2 tan 2θ 2) 2 cot θ 3) tan 2θ 4) cot 2θ Answer: (1) 2 tan 2θ Solution: tan(π/4 + θ) - tan(π/4 - θ) = [(tan π/4 + tan )/(1 - tan... View Article

1) -1 2) 0 3) 1 4) None of these Answer: (2) 0 Solution: We know that, sin(270° + x) = -cos x sin(270° - x) -cos x cos(180° + x)... View Article

1) x > 0 2) x < 0 3) x = 0 4) x ≤ 0 Answer: (1) x > 0 Solution: Given, A = 130° x = sin A + cos A x = sin 130° + cos... View Article

1) 2 2) 4 3) 8 4) 16 Answer: (3) 8 Solution: x sin 45° cos260° = (tan260° cosec 30°)/(sec 45° cot230°) x (1/√2) (1/2)2 = [(√3)2... View Article

1) 1/2 2) -1/2 3) 1/4 4) 1 Answer: (3) 1/4 Solution: we know that sin 18° = (√5 - 1)/4, cos 36° = (√5 + 1)/4 sin(π/10) sin(3π/10)... View Article

1) x = 0 2) y = 0 3) x = y 4) x = nπ - π/4 + y, (n ∈ I) Answer: (4) x = nπ - π/4 + y, (n ∈ I) Solution: Given, cos y cos(π/2 - x)... View Article

1) 1/2 2) 1 3) √2 4) 1/√2 Answer: (4) 1/√2 Solution: cos 105° + sin 105° = cos 105° + sin(90° + 15°) = cos 105° + cos 15° Using... View Article

1) 0 2) 2 sin 15° 3) cos 15° + sin 15° 4) sin 15° - cos 15° Answer: (1) 0 Solution: sin 15° + cos 105° = sin 15° + cos(90° + 15°)... View Article

1) 1/8 2) 1/4 3) (1 + √2)/2√2 4) (√2 - 1)/(√2 + 1) Answer: (1) 1/8 Solution: Given, α = 22°30' = 22 1/2° = 45°/2 = π/8 Now, (1 +... View Article

1) 0 2) 1 3) -1 4) 2 Answer: (3) -1 Solution: cos 1° + cos 2° + cos 3° + .... + cos 180° = cos 1° + cos 2° + cos 3° + ....+ cos... View Article