Answer
The expression on the left side is equal to the expression on the right side.
Work Step by Step
We have the expression on the left side $\frac{\cos x}{1-\sin x}$, which can be simplified by multiplying and dividing the expression by $1+\sin x$. As per the Pythagorean identity, ${{\sin }^{2}}x+{{\cos }^{2}}x=1$. Therefore, ${{\cos }^{2}}x=1-{{\sin }^{2}}x$.
$\begin{align}
& \frac{\cos x}{1-\sin x}=\frac{\cos x}{1-\sin x}.\frac{1+\sin x}{1+\sin x} \\
& =\frac{\cos x\left( 1+\sin x \right)}{1-{{\sin }^{2}}x} \\
& =\frac{\cos x\left( 1+\sin x \right)}{{{\cos }^{2}}x} \\
& =\frac{\left( 1+\sin x \right)}{\cos x}
\end{align}$
Hence, the expression on the left side is equal to the expression on the right side.
