Answer: pi.
- A pi
- B pi/2
- C 3pi/4
- D 2pi/3
Correct answer: A. pi
Explanation: tan-1(2)+tan-1(3) = pi + tan-1[(2+3)/(1-6)] = pi + tan-1(-1) = pi - pi/4 = 3pi/4 (since xy=6>1 and both positive, add pi). Then tan-1(1) + 3pi/4 = pi/4 + 3pi/4 = pi.
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.