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 : Simplify the following.
$\frac{\sin^3 \alpha+\cos^3 \alpha}{\sin \alpha+\cos \alpha}$

Option 1: $1+\sin \alpha \cos \alpha$

Option 2: $\tan \alpha$

Option 3: $1-\sin \alpha \cos \alpha$

Option 4: $\sec \alpha$

Question : Simplify the following expression.
$\frac{\sin \theta - 2 \sin ^3 \theta}{2 \cos ^3 \theta - \cos \theta}$

Option 1: $\tan \theta$

Option 2: $\sin \theta$

Option 3: $\sec \theta$

Option 4: $\cos \theta$

Question : If A is an acute angle, the simplified form of
$\frac{\cos (\pi-A) \cdot \cot \left(\frac{\pi}{2}+A\right) \cos (-A)}{\tan (\pi+A) \tan \left(\frac{3 \pi}{2}+A\right) \sin (2 \pi-A)}$ is:

Option 1: $ \cos^2 A$

Option 2: $\sin A$

Option 3: $\sin^2 A$

Option 4: $\cos A$

Question : Which of the following is equal to $[\frac{\tan \theta+\sec \theta–1}{\tan \theta–\sec \theta+1}]$?

Option 1: $\frac{1+\sin \theta}{\cos \theta}$

Option 2: $\frac{1+\tan \theta}{\cot \theta}$

Option 3: $\frac{1+\cot \theta}{\tan \theta}$

Option 4: $\frac{1+\cos \theta}{\sin \theta}$