Answer: pi/2.
- A pi
- B pi/2
- C 0
- D 2pi
Correct answer: B. pi/2
Explanation: For |x| >= 1, sec-1 x + cosec-1 x = pi/2, analogous to the sin-1/cos-1 identity.
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.