\(\begin{array}{l}
\frac{{1 + \cos x + \sin x}}{{1 + \cos x - \sin x}} = \frac{{1 + \sin x}}{{\cos x}}\\
\Leftrightarrow \cos x\left( {1 + \cos x + \sin x} \right) = \left( {1 + \sin x} \right)\left( {1 + \cos x - \sin x} \right)\\
\Leftrightarrow \cos x + {\cos ^2}x + \cos x\sin x = 1 + \cos x - \sin x + \sin x + \sin x\cos x - {\sin ^2}x\\
\Leftrightarrow {\cos ^2}x + {\sin ^2}x = 1\,\,\,\,\left( {luon\,\,\,dung} \right).
\end{array}\)
