Question:
If $\frac{\pi}{2} (a) sec x − tan x (b) sec x + tan x (c) tan x − sec x (d) none of these
Solution:
(c) tan x − sec x
$\sqrt{\frac{1-\sin x}{1+\sin x}}$
$=\sqrt{\frac{(1-\sin x)^{2}}{1-\sin ^{2} x}}$
$=\sqrt{\frac{(1-\sin x)^{2}}{\cos ^{2} x}}$
$=\frac{(1-\sin x)}{-\cos x} \quad\left[\operatorname{as}, \frac{\pi}{2}
$=-(\sec x-\tan x)$
$=-\sec x+\tan x$
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