Answer: -7/17.
- A -7/17
- B -17/7
- C 7/17
- D 17/7
Correct answer: A. -7/17
Explanation: Let theta = tan<sup>-1</sup>(1/5); tan 2theta = 5/12 by the double-angle formula. Then tan(2theta - pi/4) = (tan2theta - 1)/(1 + tan2theta) = -7/17.
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.