Question : If $\sin P=\frac{15}{22}$, then what is the value of $\tan P$?

Option 1: $\frac{16}{\sqrt{259}}$

Option 2: $\frac{22}{\sqrt{259}}$

Option 3: $\frac{14}{\sqrt{259}}$

Option 4: $\frac{15}{\sqrt{259}}$

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

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

Option 2: $1$

Option 3: $\frac{1}{ \sqrt{3}}$

Option 4: $\sqrt{3}$

Question : If $\tan \theta=\frac{8}{15}$, then the value of $\sqrt{\frac{1-\sin \theta}{1+\sin \theta}}$ is:

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

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

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

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

Question : If $\theta$ is an acute angle and $\sin \theta \cos \theta=2 \cos ^3 \theta-\frac{1}{4} \cos \theta$, then the value of $\sin \theta$ is:

Option 1: $\frac{\sqrt{15}-1}{8}$

Option 2: $\frac{\sqrt{15}-1}{4}$

Option 3: $\frac{\sqrt{15}+1}{4}$

Option 4: $\frac{\sqrt{15}-1}{2}$

Question : The value of $x$ in the expression $\tan^{2}\frac{\pi }{4}-\cos^{2}\frac{\pi }{3}=x\sin\frac{\pi }{4}\cos\frac{\pi }{4}\tan\frac{\pi }{3}$ is:

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

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

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

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

Question : If $\sin A-\cos A=\frac{\sqrt{3}-1}{2}$, then the value of $\sin A\cdot \cos A$ is:

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

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

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

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