Answer
See the full explanation below.
Work Step by Step
Let us consider the left side of the given expression:
$\cos \left( x-\frac{\pi }{2} \right)$
By using the identity of trigonometry, $\cos \,\left( \alpha -\beta \right)=\cos \,\alpha \,\cos \beta +\sin \,\alpha \,\sin \,\beta $, the above expression can be further simplified as:
$\begin{align}
& \cos \left( x-\frac{\pi }{2} \right)=\cos \,x\,\cos \,\frac{\pi }{2}+\sin \,x\,\sin \,\frac{\pi }{2} \\
& =\cos \,x\times 0+\sin \,x\times 1 \\
& =0+\sin \,x \\
& =\sin \,x
\end{align}$
Hence, the left side of the expression is equal to the right side, which is $\cos \left( x-\frac{\pi }{2} \right)=\sin \,x$.
