Answer: sqrt(3)/2.
- A 1/2
- B sqrt(2)/2
- C 1
- D sqrt(3)/2
Correct answer: D. sqrt(3)/2
Explanation: Use complementary identity: sin⁻¹x+cos⁻¹x=π/2. Add both equations: 2sin⁻¹x=π/2+π/6=2π/3 → sin⁻¹x=π/3 → x=sin(π/3)=√3/2. Check: cos⁻¹(√3/2)=π/6, difference=π/3−π/6=π/6 ✓.
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.