Archives

If sin^-1 x + sin^-1 (1 – x) = sin^-1 ?1 – x², then x =

1) 0, 1 / 2 2) 1, - 1 / 2 3) - 1 / 2, 1 / 2 4) none of these Solution: (1) 0, 1 / 2 Put x = sin θ sin-1 (sin θ) + sin-1 (1 - sin... View Article

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

1) - 2π / 3 2) 2π / 3 3) 4π / 3 4) None of these Solution: (4) None of these Let sin-1 [sin (2π / 3)] = θ sin θ = sin (2π / 3)... View Article

1) a + b + c = abc 2) ab + bc + ca = abc 3) 1/a + 1/b + 1/c - (1/abc) = 0 4) ab + bc + ca = a + b + c Solution: (3) 1/a + 1/b + 1/c -... View Article

1) one 2) two 3) zero 4) None of these Solution: (2) two tan-1 x + cos-1 (y) / (√1 + y2) = sin-1 (3 / √10) tan-1 x + tan-1 (1 /... View Article

1) 1 2) 2 3) 0 4) ∞ Solution: (3) 0 cos-1 x + cos-1 2x + π = 0 cos-1 x + cos-1 2x = - π cos-1 2x = - π - cos-1 x 2x = cos (π +... View Article

1) x = y = z 2) x = y = - z 3) x = 1, y = 2, z = 3 4) x = 2, y = 4, z = 6 5) x = 2, y = 3z Solution: (1) x = y = z Given x, y,... View Article

1) 6 / 17 2) 17 / 6 3) 16 / 7 4) none Solution: (2) 17 / 6 tan [cos-1 (4 / 5) + tan-1 (2 / 3)] = tan [tan-1 (3 / 4) + tan-1 (2 /... View Article

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

1) sin (cos-1 x) = cos (sin-1 x) 2) sec (tan-1 x) = tan (sec-1 x) 3) cos (tan-1 x) = tan (cos-1 x) 4) tan (sin-1 x) = sin (tan-1 x)... View Article

1) 0 2) 1/2 3) - (1/2) 4) 1 Solution: (2) 1/2 4 sin-1 x + cos-1 x = π 4 sin-1 x + [(π / 2) - sin-1 x] = π 4 sin-1 x - sin-1 x =... View Article

1) 0 2) 1 3) tan-1 x 4) tan-1 2x Solution: (3) tan-1 x tan-1 [3x - x3] / [1 - 3x2] - tan-1 [2x] / [1 - x2] tan-1 a - tan-1 b =... View Article

1) tan2 (α/2) 2) cot2 (α/2) 3) tanα 4) cot (α/2) Solution: (1) tan2 (α/2) Put √cos α = θ cot-1 θ - tan-1 θ = x (π / 2) - 2 tan-1... View Article

1) no solution 2) unique solution 3) infinite number of solutions 4) None of the above Solution: (2) unique solution sin-1 x -... View Article

1) 1/2 2) 1/√3 3) √3 4) 2 Solution: (2) 1 / √3 Put (1 / 2) tan-1 x = θ x = tan 2θ [1 - x] / [1 + x] = [1 - tan 2θ] / [1 + tan... View Article

1) 0 2) π/4 3) 1 4) π/2 Solution: (2) π/4 6x2 - 5x + 1 = 0 (α + β) = - (- 5) / 6 = 5 / 6 αβ = 1 / 6 tan-1 α + tan-1 β = tan-1... View Article

1) 49/50 2) - (49/50) 3) 24/25 4) - (24/25) 5) 48/49 Solution: (4) - (24/25) cos [2 tan-1 (-7)] 2 tan-1 x = cos-1 [1 - x2] /... View Article

1) both a and b 2) b but not a 3) a but not b 4) neither a nor b Solution: (4) neither a nor b tan-1 (a / b) + tan-1 ((a + b) / (a... View Article

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

1) 0 2) 1 3) 2 4) ∞ Solution: (1) 0 The given function is tan-1 √x (x - 1) + sin-1 √x2 + x + 1 = π / 2. The function is defined... View Article