Answer: 24/25.
- A 24/25
- B 7/25
- C 12/25
- D 3/5
Correct answer: A. 24/25
Explanation: With tanθ = 3/4, sin2θ = 2tanθ/(1 + tan²θ) = (3/2)/(25/16) = 24/25.
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.