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If (π / 2) < sin^-1 x < (π / 2), then tan (sin^-1 x) =

1) x / [1 – x2] 2) x / [1 + x2] 3) x / √1 – x2 4) 1... View Article

1) 1/2 2) 1 3) 0 4) -1/2 Solution: (4) -1/2 sin (cot-1 (1 + x)) = cos (tan-1 x)... View Article

1) – cos-1 √1 – x2 2) cos-1 √x2 – 1 3) π – cos-1 √1 – x2 4) cos-1... View Article

1) π/4 2) π/3 3) π/2 4) π/5 Solution: (1) π/4 cot-1 (2.12) + cot-1 (2.22) + cot-1 (2.32) +... View Article

1) 0 2) [√5 – 4√2] / 9 3) [√5 + 4√2] / 9 4) π/2 Solution: (3) [√5 +... View Article

1) π/2 – θ 2) θ – (π/4) 3) 2θ – (π/2) 4) π/4 – θ Solution: (2) θ –... View Article

1) 1/2 2) 1 3) -1/2 4) -1 Solution: (2) 1 sin-1 ɑ + cos-1 ɑ = π / 2... View Article

1) tan-1 5 / [1 + an-1an] 2) tan-1 5a1 / [1 + ana1] 3) tan-1 [5n – 5] /... View Article

1) -(π/3) 2) π/6 3) -(π/4) 4) π/4 5) π/2 Solution: (3) – (π / 4) sin-1{cos (4095o)} = sin-1{cos... View Article

1) 1 2) 0 3) – 1 4) π/2 Solution: (1) 1 Put x = tan θ sin [tan-1 [1... View Article

1) n / [n + 1] 2) [n + 1] / [n + 2] 3) [n + 2] / [n... View Article

1) [πab + c (a – b)] / (a + b) 2) 0 3) [πab – c (a – b)]... View Article

1) 1/3 2) 1/2 3) 1/4 4) 1/6 Solution: (2) ½ tan-1 x = π / 4 – tan-1 (1/3)... View Article

1) 0 2) 1 3) 2 4) 3 Solution: (3) 2 sin-1 x + sin-1 y + sin-1 z =... View Article

1) 4α – 4β = 0 2) 4α – 3β = 0 3) α > β 4) None of these... View Article

1) π / 4 2) π / 2 3) π 4) ∞ Solution: (1) π / 4 4 tan-1 1... View Article

1) 23/25 2) 25/23 3) 23/24 4) 24/23 Solution: (2) 25/23 cot {∑n=123 cot-1 (1 + ∑k=1n 2k)} = cot... View Article

1) zero 2) one 3) two 4) infinite Solution: (1) zero The given function is tan-1 √x (x + 1)... View Article

1) 1 / x 2) x 3) 1 / x2 4) 2x / (1 + x2) Solution: (4) 2x /... View Article

1) not defined 2) √3 3) ± 1 4) 0 Solution: (4) 0 tan-1 (x / [x + 2]) +... View Article