Answer: pi - cot-1 x.
- A cot-1 x
- B -cot-1 x
- C pi - cot-1 x
- D pi + cot-1 x
Correct answer: C. pi - cot-1 x
Explanation: Like cos-1, cot-1 is not odd; the identity is cot-1(-x) = pi - cot-1 x.
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.