Answer: sin-1(4/5).
- A sin-1(4/5)
- B sin-1(3/5)
- C sin-1(1)
- D sin-1(1/2)
Correct answer: A. sin-1(4/5)
Explanation: With x=1/2: 2x/(1+x<sup>2</sup>) = 1/(1+1/4) = 1/(5/4) = 4/5. So 2tan-1(1/2) = sin-1(4/5) (valid since |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.