Answer: x + y + z = xyz.
- A x + y + z = xyz
- B xyz = 1
- C x + y + z = 0
- D xy + yz + zx = 1
Correct answer: A. x + y + z = xyz
Explanation: Let A=tan⁻¹x, B=tan⁻¹y, C=tan⁻¹z with A+B+C=π. Then A+B=π−C, so tan(A+B)=tan(π−C)=−tanC. Expanding: (x+y)/(1−xy)=−z → x+y=−z+xyz → x+y+z=xyz. Answer: x+y+z=xyz.
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.