Question : If $\tan A = \frac{10}{15}$, then what will be the value of $\cos^2 A$?

Option 1: $\frac{59}{269}$

Option 2: $\frac{49}{269}$

Option 3: $\frac{225}{325}$

Option 4: $\frac{169}{269}$

Question : If $\tan\theta-\cot\theta=0$ and $\theta$ is positive acute angle, then the value of $\frac{\tan(\theta+15)}{\tan(\theta-15)}$ is:

Option 1: $3$

Option 2: $\frac{1}{\sqrt{3}}$

Option 3: $\frac{1}{3}$

Option 4: $\sqrt{3}$

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 : If $0°<A<90°$, the value of $\frac{\tan A\ -\ \sec A\ -\ 1}{\tan A\ +\ \sec A\ +\ 1}$ is:

Option 1: $\frac{\sin A-1}{\cos A}$

Option 2: $\frac{1-\sin A}{\cos A}$

Option 3: $\frac{1-\cos A}{\sin A}$

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

Question : If $\cos \theta=\frac{\sqrt{3}}{2}$, then $\tan ^2 \theta \cos ^2 \theta=?$

Option 1: $\frac{1}{\sqrt{3}}$

Option 2: $\frac{1}{4}$

Option 3: $\frac{1}{2}$

Option 4: $\sqrt{3}$

Question : If $\tan \frac{A}{2}=x$, then find $x$.

Option 1: $\frac{\sqrt{1+\cos A}}{\sqrt{1-\cos A}}$

Option 2: $\frac{\sqrt{1-\sin A}}{\sqrt{1+\cos A}}$

Option 3: $\frac{\sqrt{1-\cos A}}{\sqrt{1+\cos A}}$

Option 4: $\frac{\sqrt{\cos A-1}}{\sqrt{1+\cos A}}$