Question : The value of $\sec x - \cos x = $?
Option 1: $\tan x \sin x$
Option 2: $\sec x \tan x$
Option 3: $\tan x \cos x$
Option 4: $\sec x \cos x$
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Correct Answer: $\tan x \sin x$
Solution :
$\sec x - \cos x$
$ = \frac{1}{\cos x} - \cos x $
$ = \frac{1- \cos ^{2}x}{\cos x}$
$ = \frac{\sin^{2}x}{\cos x}$
$ = \frac{\sin x }{\cos x}\times \sin x$
$ = \tan x \sin x$
Hence, the correct answer is $\tan x \sin x$.
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