Answer: pi/4 - x/2.
- A pi/4 - x/2
- B pi/4 + x/2
- C x/2
- D pi/2 - x
Correct answer: A. pi/4 - x/2
Explanation: Using half-angle substitutions, cos x/(1+sin x) simplifies to tan(pi/4 - x/2), so the expression equals pi/4 - x/2 within the valid principal range.
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.