Inverse Trigonometric Functions

The value of tan(sin⁻¹(8/17)) is

1. 8/15
2. 15/8
3. 17/15
4. 8/17

If sin⁻¹x = π/6, then x equals

1. 1/2
2. √3/2
3. −1/2
4. −√3/2

The value of cos(2 tan⁻¹1) is

1. 1
2. 0
3. −1
4. 1/2

The principal value of sec⁻¹(−2) is

1. π/3
2. 2π/3
3. −π/3
4. −2π/3

The domain of sin⁻¹x is

1. (−∞, ∞)
2. [−1, 1]
3. (−1, 1)
4. [0, 1]

If θ = tan⁻¹(1) + tan⁻¹(√3), then θ equals

1. π/3
2. π/2
3. 3π/4
4. π

The value of cos(2 sin⁻¹(1/2)) is

1. 1
2. 1/2
3. 0
4. −1/2

The value of sin(tan⁻¹(3/4)) is

1. 3/5
2. 4/5
3. 5/3
4. 4/3

The value of tan(cos⁻¹(4/5)) is

1. 3/4
2. 4/3
3. 5/4
4. 3/5

The value of cos(sin⁻¹(5/13)) is

1. 5/13
2. 12/13
3. −12/13
4. 13/12

The value of sin(cos⁻¹(3/5)) is

1. 3/5
2. 4/5
3. −4/5
4. 5/4

The value of tan⁻¹(1) is

1. 0
2. π/6
3. π/4
4. π/2

The value of cos⁻¹(−1/2) is

1. π/3
2. 2π/3
3. 4π/3
4. 5π/3

The principal value of sin⁻¹(−√3/2) is

1. −π/3
2. −π/2
3. −π/6
4. −π/3

[IMAGE REQUIRED] For x > 0, if the value of tan⁻¹(x) + tan⁻¹(1/x) is

1. 0
2. π/2
3. π
4. -π/2

If tan⁻¹(1/2) + tan⁻¹(2/11) = tan⁻¹(λ), then λ is equal to

1. 1/4
2. 3/4
3. 15/22
4. None of these

The number of solutions of sin⁻¹x + sin⁻¹2x = π/3 is

1. 0
2. 1
3. 2
4. Infinite

If α and β are roots of ax² + bx + c = 0, the value of tan⁻¹α + tan⁻¹β is

1. tan⁻¹(b/a)
2. tan⁻¹(a/c)
3. tan⁻¹(c/a)
4. tan⁻¹(b/(a-c))

The value of sin⁻¹(cos(33π/5)) is

1. 3π/5
2. -π/10
3. π/10
4. 7π/5

The equation sin⁻¹x + cos⁻¹x + tan⁻¹x = π has

1. 3 roots whose sum is zero
2. 2 roots
3. 3 roots which are in G.P.
4. 3 roots which are in H.P.

The value of tan⁻¹(tan(3π/4)) is

1. 3π/4
2. -π/4
3. π/4
4. None of these

The number of solutions of 2sin⁻¹(x) - tan⁻¹x = π is

1. 2
2. 3
3. 1
4. None of these

If in triangle ABC, tan⁻¹A + tan⁻¹B = π/4, then angle C is equal to

1. π/6
2. π/4
3. π/3
4. None of these

The function f(x) = sin⁻¹(2x + 2) is an increasing function in

1. (-∞, ∞)
2. (-3/2, -1/2)
3. (0, 1)
4. None of these

The largest interval lying in (-π/2, π/2) for which f(x) = 4⁻ˣ² + cos⁻¹(x/2 - 1) + log(cosx) is defined, is

1. [0, π]
2. (-π/2, π/2)
3. [0, π/2)
4. [0, π/2]

If the equation tan⁻¹(x+1) + tan⁻¹(x-1) = tan⁻¹(8/31), then x is equal to

1. -1/4
2. 1/4
3. 4
4. None of these

The value of sin(2sin⁻¹(0.6)) is

1. 0.48
2. 0.96
3. 0.6
4. None of these

If 0 < x < 1, the number of solutions of 3tan⁻¹x + cos⁻¹(2x²-1) = π is

1. 0
2. 1
3. 2
4. 3

The equation tan⁻¹x + tan⁻¹y = π/4 has

1. No solution
2. Unique solution
3. Infinite number of solutions
4. None of these

cos⁻¹(cos(17π/6)) is equal to

1. π/6
2. 17π/6
3. 5π/6
4. None of these

If sin⁻¹x + sin⁻¹y + sin⁻¹z = π, then x + y + z is equal to

1. π/2
2. xyz
3. xy + yz + zx
4. None of these

If tan⁻¹ = tan⁻¹(2+k) + π/2 has at least one solution for θ ∈ [0, 2π], k ∈ integers, the number of integral values of k is

1. 0
2. 1
3. 2
4. 3

The principal value of sin⁻¹(sin(2π/3)) is

1. 2π/3
2. π/3
3. -π/3
4. None of these

The number of solutions of the equation sin⁻¹x + sin⁻¹(1-x) = cos⁻¹x is

1. 2
2. 3
3. 1
4. None of these

The number of positive integral solutions of abc = 30 is

1. 30
2. 27
3. 8
4. None of these

The sum of the series cot⁻¹2 + cot⁻¹8 + cot⁻¹18 + cot⁻¹32 + … is

1. π/4
2. π/4
3. π/2
4. π

The number of real solutions of √(x(x+1)) + sin⁻¹√(x²+x+1) = π/2 is

1. Zero
2. One
3. Two
4. Infinite

If f(x) = sin⁻¹(cosec(sin⁻¹x)) + cos⁻¹(sec(cos⁻¹x)) has

1. Exactly two values
2. One value
3. Undefined
4. Infinite values

If k ≤ sin⁻¹x + cos⁻¹x + tan⁻¹x ≤ K for x ∈ [-1, 1], then

1. k = 0, K = π
2. k = π/4, K = 3π/4
3. k = -π/4, K = π/4
4. None of these

Range of f(x) = sin⁻¹x + tan⁻¹x + cos⁻¹x is

1. (0, π)
2. [0, π]
3. {π/2}
4. [π/4, 3π/4]

The number of real solutions of cos⁻¹x + cos⁻¹2x = π is

1. 0
2. 1
3. 2
4. Infinitely many

The value of tan⁻¹1 + tan⁻¹2 + tan⁻¹3 is

1. 0
2. 1
3. π
4. π/2

The value of cos(2cos⁻¹0.8) is

1. 0.48
2. 0.96
3. 0.6
4. 0.28

If tan⁻¹n + cot⁻¹(n+1) = tan⁻¹x, then x is

1. n² + 1
2. n + 1
3. n² + n + 1
4. None of these

The number of triplets (x, y, z) satisfying sin⁻¹x + cos⁻¹y + sin⁻¹z = 2π is

1. 0
2. 2
3. 1
4. None of these