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Tan Inverse X Y Minus Tan Inverse X Minus Y

1) π/2 2) π/3 3) π/4 4) π/4 or -3π/4 Answer: (3) π/4 Solution: tan-1(x/y) - tan-1[(x - y)/(x + y)] Using the formula tan-1(a) -... View Article

1) xy + zy + zt 2) 1 - 2xyzt 3) 4 4) 6 Answer: (3) 4 Solution: We know that, 0 ≤ cos-1(x) ≤ π Thus, the maximum value of cos-1(x)... View Article

1) 2π/3 2) π/3 3) π/6 4) π Answer: (2) π/3 Solution: Given, sin-1(x) + sin-1(y) = 2π/3 Using the formula sin-1(x) + cos-1(x) =... View Article

1) π/2 2) π/3 3) π/4 4) None of these Answer: (3) π/4 Solution: 4 tan-1(1/5) - tan-1(1/70) + tan-1(1/99) = 2[2 tan-1(1/5)] -... View Article

1) π 2) π/2 3) 0 4) None of these Answer: (2) π/2 Solution: Let A = sin-1x x = sin A = cos(π/2 - A) Now, sin-1(x) + cos-1(x) =... View Article

1) π/4 2) π/6 3) π/3 4) 2π/3 Answer: (4) 2π/3 Solution: cos-1(1/2) + 2 sin-1(1/2) = cos-1(cos π/3) + 2 sin-1(sin π/6) = (π/3) +... View Article

1) (a - b)/(1 + ab) 2) b/(1 + ab) 3) b/(1 - ab) 4) (a + b)/(1 - ab) Answer: (4) (a + b)/(1 - ab) Solution: Given, sin-1[2a/(1 +... View Article

1) α + β 2) α - β 3) (1 + αβ)/(α + β) 4) (αβ - 1)/(α + β) Answer: (4) (αβ - 1)/(α + β) Solution: Given, cot-1(α) + cot-1(β) =... View Article

1) π/6 2) π/4 3) π/3 4) π/2 Answer: (2) π/4 Solution: Let sin-1(1/√5) = A sin A = 1/√5 Using the identity sin2x + cos2x = 1,... View Article

1) 135° 2) 45° 3) 90° 4) 180° Answer: (1) 135° Solution: Given, x = 2, y = 3 As x > 0, y > 0 xy > 1 So, tan-1(x) +... View Article

1) 7/3 2) 3 3) 11/3 4) 13/3 Answer: (4) 13/3 Solution: Given, tan-1(1/3) + tan-1(3/4) - tan-1(x/3) = 0 tan-1(1/3) + tan-1(3/4) =... View Article

1) π/4 2) π/2 3) π 4) 0 Answer: (2) π/2 Solution: Let x = tan A tan-1[(1 - x2)/2x] + cos-1[(1 - x2)/(1 + x2)] = tan-1[(1 -... View Article

1) π/3 2) π/4 3) π/6 4) π/2 Answer: (2) π/4 Solution: Let cosec-1(√5) = A cosec A = √5 Using the identity cosec2x - cot2x = 1,... View Article

1) 0 2) 1 3) -1 4) 2 Answer: (2) 1 Solution: Given, cos-1(3/5) - sin-1(4/5) = cos-1(x)....(i) Let sin-1(4/5) = A sin A = 4/5... View Article

1) 2√3a 2) √3a 3) 2√3a2 4) None of these Answer: (1) 2√3a Solution: Given, tan-1[(a + x)/a] + tan-1[(a - x)/a] = π/6 Using the... View Article

1) 0 2) 1 3) cot-1(x) + cot-1(y) + cot-1(z) 4) None of the above Answer: (1) 0 Solution: cot-1[(xy + 1)/(x - y)] + cot-1[(yz +... View Article

1) tan-1(x2 + 1) 2) tan-1(x2 + x) 3) tan-1(x + 1) 4) tan-1(x2 + x + 1) Answer: (4) tan-1(x2 + x + 1) Solution: tan-1(x) + cot-1(x +... View Article

1) 1/√2 2) √3/2 3) 1/2 4) π/4 Answer: (1) 1/√2 Solution: tan-1(1/3) + tan-1(1/2) Using the formula tan-1(x) + tan-1(y) = tan-1[(x... View Article

1) π/2 2) 2π/3 3) 5π/3 4) None of these Answer: (1) π/2 Solution: Let 2 sin-1(3/5) = A sin-1(3/5) = A/2 sin A/2 = 3/5 Using the... View Article

1) 1/3 2) 1/4 3) 3 4) 4 Answer: (3) 3 Solution: Given, cot-1(x) + tan-1(3) = π/2 We know that tan-1(x) + cot-1(x) = π/2... View Article