Question : $\frac{\cos A}{1-\tan A}+\frac{\sin A}{1-\cot A}=$___________.

Option 1: $\tan A - \cot A$

Option 2: $\tan A + \cot A$

Option 3: $\sin A - \cos A$

Option 4: $\sin A + \cos A$

Question : Which of the following is equal to $\sec A – \cos A$?

Option 1: $\sin A\cot A$

Option 2: $\cot A\ cos A$

Option 3: $\tan  A\sin A$

Option 4: $\cos A\sin A$

Question : What will be the value of $\cos x \operatorname{cosec} x - \sin x \sec x$?

Option 1: $\cot \frac{2x}{2}$

Option 2: $\tan 2 x $

Option 3: $\cot 2 x $

Option 4: $ 2 \cot 2x$

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: $\sec x \cos x$

Question : Simplify:
$\frac{\cos A}{1+\tan A}-\frac{\sin A}{1+\cot A}$

Option 1: $\tan A$

Option 2: $\cos A-\sin A$

Option 3: $\cos A \sin A$

Option 4: $\cos A+\sin A$