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📐 Mathematics  ·  Inverse Trigonometric Functions  ·  JEE

For all x in [−1, 1], sin⁻¹(x) + cos⁻¹(x) equals:

Answer: π/2.

  • A π/2
  • B π
  • C 0
  • D π/4

Correct answer: A. π/2

Explanation: sin⁻¹(x) + cos⁻¹(x) = π/2 is a standard identity.

y = sin⁻¹x: Principal Value Branchxyx=-1x=1y=-π/2y=π/2Domain restricted to [-1,1]; range restricted to [-π/2,π/2] - this restriction is what makes the inverse exist

The graph of sin⁻¹x is confined to a narrow domain [-1,1] (since sine itself only takes values in that range) and range [-π/2,π/2] (the principal value branch chosen to make sine one-one and invertible there).

Concept context

Restricting trig functions to make them invertible, the principal value branches of sin-inverse, cos-inverse, tan-inverse, and friends, and the key identities relating them.

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