Answer: π/4.
- A π/6
- B π/4
- C π/3
- D π/2
Correct answer: B. π/4
Explanation: Using the sum formula, ((1/2 + 1/3)/(1 − 1/6)) = 1, so the sum is arctan1 = π/4.
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.