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:
$\frac{\cos x-\sqrt{3} \sin x}{2}$

Option 1: $\cos \left(\frac{\pi}{3}-x\right)$

Option 2: $\sin \left(\frac{\pi}{3}+x\right)$

Option 3: $\cos \left(\frac{\pi}{3}+x\right)$

Option 4: $\sin \left(\frac{\pi}{3}-x\right)$

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: $\cos A+\sin A$

Question : Evaluate the following:
$\cos \left(36^{\circ}+A\right) \cdot \cos \left(36^{\circ}-A\right)+\cos \left(54^{\circ}+A\right) \cdot \cos \left(54^{\circ}-A\right)$

Option 1: $\sin 2A$

Option 2: $\cos A$

Option 3: $\sin A$

Option 4: $\cos 2A$

Question : $\frac{1+\sin \theta}{\cos \theta}$ is equal to which of the following (where $\left.\theta \neq \frac{\pi}{2}\right)?$

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

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

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

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