# How do you simplify sin^-1(sin (1/6)(pi))?

$\frac{\pi}{6}$.
$\sin \mathmr{and} {\sin}^{- 1}$ are each inverse of the other.
So, applied in succession, both $\sin {\sin}^{- 1} \mathmr{and} {\sin}^{- 1} \sin$ return the operand.
$\sin {\sin}^{- 1} x = x \mathmr{and} \sin {\sin}^{- 1} y = y$