Answer: x = y = z = -1.
- A x = y = z = 0
- B x = y = z = 1
- C x = y = z = -1
- D x + y + z = 0
Correct answer: C. x = y = z = -1
Explanation: Since each cos-1 term has a maximum value of pi (attained only when the argument is -1), the sum equals 3pi only when x=y=z=-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.