Answer: tan-1(3/4).
- A tan-1(3/4)
- B tan-1(2/3)
- C tan-1(1/2)
- D tan-1(4/3)
Correct answer: A. tan-1(3/4)
Explanation: With x=1/3: 2x/(1-x<sup>2</sup>) = (2/3)/(1-1/9) = (2/3)/(8/9) = (2/3)(9/8) = 3/4. So 2tan-1(1/3) = tan-1(3/4) (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.