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tan^-1 x / ?a² – x²

1) (1 / a) sin-1 (x / a) 2) a sin-1 (x / a) 3) sin-1 (x / a) 4) sin-1 (a / x) Solution: (3) sin-1 (x / a) tan-1 x / √a2 - x2 =... View Article

1) tan-1 x 2) (1 / 2) tan-1 x 3) 2 tan-1 x 4) None of these Solution: (2) (1 / 2) tan-1 x tan-1 [(√1 + x2) - 1] / x = tan-1 [(√1... View Article

1) √3 2) 1 / √3 3) 1 / √2 4) None of these Solution: (2) 1 / √3 sin-1 (1 / 2) = tan-1 x tan-1 x = π / 6 x = tan 30o = 1 / √3... View Article

1) 1 / 2x 2) x2 3) 1 / x2 4) 2 / x Solution: (3) 1 / x2 Let sin-1 x = θ sin θ = x 1 + cot2 θ = cosec2 θ = 1 / x2 1 + cot2... View Article

1) - π / 6 2) 5π / 6 3) π / 3 4) 2π / 3 Solution: (2) 5π / 6 cot-1 (- √3) = π - cot-1 (√3) = 5π / 6... View Article

1) 12 / 13 2) - 12 / 13 3) 5 / 12 4) None of these Solution: (1) 12 / 13 Let sin-1 (5 / 13) = x sin x = 5 / 13 cos x = √1 - (25... View Article

1) √1 + x2 2) x 3) (1 + x2)-3/2 4) (1 + x2)-1/2 Solution: (4) (1 + x2)-1/2 Let cot-1 x = θ x = cot θ cosec θ = √1 - cot2 θ = √1... View Article

1) 1 / √x2 - 1 2) √x2 + 1 3) √1 - x2 4) √x2 - 1 Solution: (4) √x2 - 1 cos-1 (1 / x) = θ cos θ = 1 / x tan θ = sin θ / cos θ =... View Article

1) sin-1 (1 / 2) - sin-1 x 2) sin-1 x - (π / 6) 3) sin-1 x + (π / 6) 4) none of these Solution: (2) sin-1 x - (π / 6) Let x = sin... View Article

1) 3π / 10 2) 17π / 20 3) 7π / 10 4) none of these Solution: (2) 17π / 20 {(1 / √2) [cos (9π / 10) - sin (9π / 10)]} = cos [(π /... View Article

1) 0 2) 1 3) 2 4) ∞ Solution: (3) 2 The given equation becomes |cos x| = sin-1 (sin x) If - π / 2 ≤ x ≤ π / 2, cos x = x In this... View Article

1) [-1, 1] 2) [0, 1 / 2] 3) [-1, 0] 4) none of these Solution: (4) none of these sin-1 x, cos-1 x exist for - 1 ≤ x ≤ 1 But for... View Article

1) 2 2) 4 3) 0 4) none of these Solution: (4) none of these (π / 2) + sin-1 y - cos-1 y = π / 3 π - 2 cos-1 y = π / 3 cos-1 y =... View Article

1) f (2 / 3) = π / 3 2) f (2 / 3) = 2 cos-1 (2 / 3) - (π / 3) 3) f (1 / 3) = π / 3 4) f (1 / 3) = (π / 3) + 2 cos-1 (1 / 3)... View Article

1) f (8π / 9) = e13π/18 2) f (8π / 9) = e5π/18 3) f (- 7π / 4) = e7π/12 4) f (- 7π / 4) = e11π/12 Solution: (1) f (8π / 9) = e13π/18... View Article

1) √5 / 3 2) 3 / √5 3) 2 / √5 4) √5 / 2 Solution: (2) 3 / √5 tan (sec-1 x) = √sec2 (sec-1 x - 1) = sin (sin-1 [2 / √5]) cos-1 1 /... View Article

1) nπ - (π / 4), n ∈ I 2) nπ + (π / 4), n ∈ I 3) 2nπ - (π / 4), n ∈ I 4) 2nπ + (π / 4), n ∈ I Solution: (2) nπ + (π / 4), n ∈ I 2... View Article

1) π / 3 2) π / 4 3) π / 2 4) π / 6 Solution: (3) π / 2 LHS = tan-1 [5 + 3] / [1 - 5 * 3] - cot-1 (4 / 7) = tan-1 (8 - 14) -... View Article

1) 7π / 12 2) 17π / 12 3) 5π / 12 4) π / 12 Solution: (2) 17π / 12 sin-1 (- √2 / 2) + cos-1 (- 1 / 2) - tan-1 (- √3) + cot-1 (- 1... View Article

1) 1 2) 0 3) -1 4) 2 Solution: (2) 0 √(2 - √3) / 4 = √4 - 2√3) / 8 = √(√3 - 1)2 / 8 = [√3 - 1] / 2√2 sin-1 √(2 - √3) / 4 = sin-1... View Article