sin(sin^(-1)(x)) = x for all x in [-1, 1] — this always simplifies. But sin^(-1)(sin(x)) = x ONLY when x is in [-pi/2, pi/2]. For other x, you must reduce to the principal value branch. Example: sin^(-1)(sin$\frac{5*pi}{6}$) = sin^(-1)$\frac{1}{2}$ = pi/6 $\frac{not 5*pi}{6}$. This is a very common JEE trap.