Answer: 2x/(1 − x²).
- A 2x/(1 − x²)
- B simply x²
- C simply 2x
- D simply x/2
Correct answer: A. 2x/(1 − x²)
Explanation: 2 tan⁻¹(x) = tan⁻¹(2x/(1 − x²)) for |x| < 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.