Trigonometry Inverse Trigonometric Mock Tests

Considering only principal values, the number of real solutions x to the equation sin⁻¹(x² − 1) + cos⁻¹(1 − x²) + tan⁻¹(x − 1) = π/2 is:

Considering only the principal values of the inverse trigonometric functions, the value of cos^-1(1/2) + sin^-1(sqrt(3)/2) + tan^-1(1) is

The number of real solutions of the equation sin⁻¹(x) + sin⁻¹(2x) = π/3 is:

If cos⁻¹(1/√2) + sin⁻¹(√2/2) + tan⁻¹(1) = θ, where θ is in the principal range, then sin(θ) is:

Considering only the principal values of the inverse trigonometric functions, the value of cos^-1(sqrt(1/2)) + sin^-1(sqrt(2)/2) + tan^-1(1) is equal to:

Considering only principal values, the number of real solutions to cos⁻¹(x) + cos⁻¹(2x) = π is:

Considering only principal values, the value of sin^-1(1/2) + cos^-1(1/2) + tan^-1(1/sqrt(3)) is