Answer: pi/4.
- A pi/4
- B pi/3
- C pi/2
- D pi/6
Correct answer: A. pi/4
Explanation: Using tan-1 x + tan-1 y = tan-1[(x+y)/(1-xy)] with x=1/2, y=1/3: (1/2+1/3)/(1-1/6) = (5/6)/(5/6) = 1. So the sum is tan-1(1) = pi/4 (valid since xy=1/6<1).
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.