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 : If $\theta$ is an acute angle and $\sin \theta=\frac{13}{19}$, what is the value of $\cos \theta?$

Option 1: $\frac{6}{19}$

Option 2: $\frac{10 \sqrt{2}}{19}$

Option 3: $\frac{14}{19}$

Option 4: $\frac{8 \sqrt{3}}{19}$

Question : If $2(\cos^{2}\theta-\sin^{2}\theta)=1$; ($\theta$ is a positive acute angle), then $\cot\theta$ is equal to:

Option 1: $–\sqrt{3}$

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

Option 3: $1$

Option 4: $\sqrt{3}$

Question : If $\theta$ is an acute angle and $\sin \theta=\frac{21}{25}$, then what is the value of $\tan \theta$?

Option 1: $\frac{2 \sqrt{46}}{21}$

Option 2: $\frac{25}{2 \sqrt{46}}$

Option 3: $\frac{21}{2 \sqrt{46}}$

Option 4: $\frac{2 \sqrt{46}}{25}$

Question : If $\theta$ be an acute angle and $\tan \theta+\cot \theta=2$, then the value of $2 \tan ^2 \theta+\cot ^2 \theta+\tan ^4 \theta \cot ^4 \theta$ is:

Option 1: 4

Option 2: 2

Option 3: 3

Option 4: 6