Inverse Trigonometric Functions

Find the value of sin⁻¹[sin(3π⁄5)]
1. 2π⁄5
2. 3π⁄10
3. 3π⁄5
4. None
cot⁻¹x =
1. cos⁻¹(¹⁄ₓ)
2. sin⁻¹(¹⁄ₓ)
3. tan⁻¹(¹⁄ₓ)
4. cosec⁻¹(¹⁄ₓ)
If sin⁻¹x = y, then
1. 0 ≤ y ≤ π
2. −π⁄2≤y≤π⁄2
3. 0 < y < π
4. -π⁄2<y<π⁄2
tan⁻¹(√3)−sec⁻¹(2) is equal to
1. π
2. -π/3
3. π/3
4. 2π/3
The principal value of sin⁻¹[sin(2π⁄₃)]
1. -2π⁄3
2. 2π⁄3
3. 4π⁄3
4. None of these
If θ = tan⁻¹a , φ = tan⁻¹b and ab=−1, then θ−φ=
1. 0
2. π⁄4
3. π⁄2
4. None
If tan(cos⁻¹x)=sin(cot⁻¹(½)),then x=
1. ±⁵⁄₃
2. ±√⁵⁄₃
3. ±⁵⁄√₃
4. None
If sin⁻¹x=π/5 for some x∈(−1,1), then the value of cos⁻¹x is
1. 3π⁄10
2. 5π⁄10
3. 7π⁄10
4. 9π⁄10
If cos⁻¹p + cos⁻¹q + cos⁻¹r=π then p² + q² + r² + 2pqr =
1. 3
2. 1
3. 2
4. -1
If tan⁻¹x+tan⁻¹y+tan⁻¹z=π, then x+y+z is equal to
1. xyz
2. 0
3. 1
4. 2xyz
2tan⁻¹(cosx)=tan⁻¹(cosec²x), then x =
1. π⁄2
2. π
3. π⁄6
4. π⁄3
cosec⁻¹x =
1. cos⁻¹(¹⁄ₓ)
2. sin⁻¹(¹⁄ₓ)
3. cot⁻¹(¹⁄ₓ)
4. cot⁻¹(¹⁄ₓ)
sec⁻¹x =
1. cos⁻¹(¹⁄ₓ)
2. sin⁻¹(¹⁄ₓ)
3. tan⁻¹(¹⁄ₓ)
4. sec(¹⁄ₓ)
Find the principal value of sin⁻¹(¹⁄√₂)
1. π⁄4
2. π⁄2
3. π
4. π⁄6
Find the principal value of cot⁻¹(¹⁄√3)
1. 2π
2. 2π/3
3. π⁄2
4. π
sin⁻¹(1 – x) – 2sin⁻¹x = π/2, then x is equal to
1. 0,½
2. 1,½
3. 0
4. ½
tan⁻¹(x/y) - tan⁻¹(x-y/x+y) is equal to
1. π/2
2. π/3
3. π/4
4. -3π/4
sin (tan⁻¹x), | x | < 1 is equal to
1. x⁄(√1-x²)
2. 1⁄(√1-x²)
3. 1⁄(√1+x²)
4. 1⁄(√1+x²)
If function y = tan⁻¹x ,domain R then principal value branch is
1. [-π⁄₂,π⁄₂]
2. [0, π]-[π⁄₂]
3. [-π⁄₂,π⁄₂]– {0}
4. (0, π)
If function y = sec⁻¹x ,domain (-1,1) then principal value branch is
1. [-π⁄₂,π⁄₂]
2. [0, π]-[π⁄₂]
3. [-π⁄₂,π⁄₂]– {0}
4. (0, π)
If function y = cosec⁻¹x ,domain (-1,1) then principal value branch is
1. [-π⁄₂,π⁄₂]
2. [0, π]-[π⁄₂]
3. [-π⁄₂,π⁄₂]– {0}
4. (0, π)
If function y = cot⁻¹x ,domain R then principal value branch is
1. [-π⁄₂,π⁄₂]
2. [0, π]-[π⁄₂]
3. [-π⁄₂,π⁄₂]– {0}
4. (0, π)

Inverse Trigonometric Functions

Quiz