Answer
$\Rightarrow \cos ^{-1}\left( \cos \left( \dfrac {\pi }{4}\right) \right) =\dfrac {\pi }{4}$
Work Step by Step
$\cos ^{-1}\left( \cos \left( x\right) \right) =x\left( 0\leq x\leq \pi \right) $
$\Rightarrow \cos ^{-1}\left( \cos \left( \dfrac {\pi }{4}\right) \right) =\dfrac {\pi }{4}$