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 : If $\sin \theta=\frac{8}{17}$, then find the value of $\tan \theta$.

Option 1: $\frac{15}{17}$

Option 2: $\frac{8}{15}$

Option 3: $\frac{15}{8}$

Option 4: $\frac{17}{15}$

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 $\tan\theta +\cot\theta =2$, then the value of $\left (\tan^{n}\theta+\cot^{n}\theta \right)$ is:

Option 1: $2^{n}$

Option 2: $2^{\frac{n}{2}}$

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

Option 4: $2$

Question : If $8 \cot A = 7$, then find $\sin A$.

Option 1: $\frac{7}{15}$

Option 2: $\frac{8}{\sqrt{113}}$

Option 3: $\frac{7}{8}$

Option 4: $\frac{8}{7}$