The Value Of Sin Inverse Root 3 2 Minus Sin Inverse 1 2 Is 1) 45° 2) 90° 3) 15° 4) 30° Answer: (4) 30° Solution: sin-1(√3/2) - sin-1(1/2) As we know sin 60° = √3/2 and sin 30° = 1/2. =... View Article
Sin Tan Inverse 1 Minus X Square 2x Plus Cos Inverse 1 Minus X Square 1 1) 0 2) 1 3) √2 4) 1/√2 Answer: (2) 1 Solution: Let x = tan A tan-1[(1 - x2)/2x] + cos-1[(1 - x2)/(1 + x2)] = tan-1[(1 - tan2A)/2... View Article
If Sin Inverse 3 5 Plus Cos Inverse 12 13 Sin Inverse C Then 1) 65/56 2) 24/65 3) 16/65 4) 56/65 Answer: (4) 56/65 Solution: Let cos-1(12/13) = A cos A = 12/13 Using the identity sin2x +... View Article
If 4 Sin Inverse X Plus Cos Inverse X Pi Then X Is 1) 0 2) 1/2 3) -√3/2 4) 1/√2 Answer: (2) 1/2 Solution: Given, 4 sin-1(x) + cos-1(x) = π 3 sin-1(x) + sin-1(x) + cos-1(x) = π 3... View Article
The Value Of Cos Inverse Cos 5pi 3 Plus Sin Inverse Sin 5pi 3 Is 1) 0 2) π/2 3) 2π/3 4) 10π/3 Answer: (1) 0 Solution: cos-1(cos 5π/3) + sin-1(sin 5π/3) = cos-1[cos(2π - π/3)] + sin-1[sin(2π -... View Article
If Sin Inverse A Sin Inverse B Sin Inverse C Pi Then 1) 2abc 2) abc 3) (1/2)abc 4) (1/3)abc Answer: (1) 2abc Solution: Given, sin-1(a) + sin-1(b) + sin-1(c) = π Let sin-1(a) = x,... View Article
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
If Cos Inverse X Plus Cos Inverse Y Plus Cos Inverse Z Cos Inverse T 4pi Then 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
If Sin Inverse X Plus Sin Inverse Y 2pi 3 Then 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
4 Tan Inverse 1 5 Minus Tan Inverse 1 70 Plus Tan Inverse 1 99 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
For A Real X The Angle Sin Inverse Plus Cos Inverse Equals 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
Cos Inverse 1 2 Plus 2 Sin Inverse 1 2 Is 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
If Sin Inverse 2a 1 Plus A Square Plus Sin Inverse 2b 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
If Cot Inverse Alpha Plus Cot Inverse Beta 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
Sin Inverse 1 Root5 Plus Cot Inverse 3 Is 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
For X 2 And Y 3 The Angle Tan Inverse X Plus Tan Inverse Y 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
If Tan Inverse 1 3 Plus Tan Inverse 3 4 Minus Tan Inverse X 3 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
Tan Inverse 1 X Square 2x Plus Cos Inverse 1 X Square 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
Cot Inverse 3 Plus Cosec Inverse Root5 Equals To 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
If Cos Inverse 3 5 Minus Sin Inverse 4 5 Cos Inverse X 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