Question : If $\sin \theta=\frac{3}{5}$, then what is $\tan \theta ?$

Option 1: $\frac{3}{5}$

Option 2: $\frac{4}{3}$

Option 3: $\frac{4}{5}$

Option 4: $\frac{3}{4}$

Question : If $\sqrt{3} \tan \theta=3 \sin \theta$, then what is the value of $\sin ^2 \theta-\cos ^2 \theta$?

Option 1: $\frac{1}{5}$

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

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

Option 4: $\frac{1}{3}$

Question : If $\tan\theta=1$, then the value of $\frac{8\sin\theta\:+\:5\cos\theta}{\sin^{3}\theta\:–\:2\cos^{3}\theta\:+\:7\cos\theta}$ is:

Option 1: $2$

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

Option 3: $3$

Option 4: $\frac{4}{5}$

Question : What is $\tan \frac{\theta}{2}$?

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

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

Option 3: $\frac{\cos \theta}{1-\cos \theta}$

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

Question : If $\frac{\sin ^2 \theta}{\cos ^2 \theta-3 \cos \theta+2}=1, \theta$ lies in the first quadrant, then the value of $\frac{\tan ^2 \frac{\theta}{2}+\sin ^2 \frac{\theta}{2}}{\tan \theta+\sin \theta}$ is:

Option 1: $\frac{2 \sqrt{3}}{27}$

Option 2: $\frac{5 \sqrt{3}}{27}$

Option 3: $\frac{2 \sqrt{3}}{9}$

Option 4: $\frac{7 \sqrt{3}}{54}$

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