Answer: π/2.
- A π/2
- B exactly π
- C exactly 0
- D exactly 2π
Correct answer: A. π/2
Explanation: sec⁻¹(x) + cosec⁻¹(x) = π/2, analogous to the other complementary identities.
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.