Answer
As left side transforms into right side, hence given identity-
$\frac{1 - \sec x}{1 + \sec x} $ = $ \frac{\cos x - 1}{\cos x + 1}$ is true.
Work Step by Step
Given identity is-
$\frac{1 - \sec x}{1 + \sec x} $ = $ \frac{\cos x - 1}{\cos x + 1}$
Taking L.S.
$\frac{1 - \sec x}{1 + \sec x} $
= $\frac{1 - \frac{1}{\cos x} }{1 + \frac{1}{\cos x} } $
= $\frac{\frac{\cos x}{\cos x} - \frac{1}{\cos x} }{\frac{\cos x}{\cos x} + \frac{1}{\cos x} } $
= $\frac{\frac{\cos x -1}{\cos x} }{\frac{\cos x + 1}{\cos x} } $
= $\frac{(\cos x -1)\cos x} {(\cos x + 1)\cos x} $
= $ \frac{\cos x - 1}{\cos x + 1}$
= R.S.
As left side transforms into right side, hence given identity-
$\frac{1 - \sec x}{1 + \sec x} $ = $ \frac{\cos x - 1}{\cos x + 1}$ is true.
