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 $\tan\theta+\sec\theta=3$, $\theta$ being acute, the value of $5\sin\theta$ is:

Option 1: $\frac{5}{2}$

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

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

Option 4: $4$

Question : If $\tan\theta =\frac{3}{4}$, then the value of $\frac{4\sin^{2}\theta–2\cos^{2}\theta}{4\sin^{2}\theta+3\cos^{2}\theta}$ is equal to:

Option 1: $\frac{1}{21}$

Option 2: $\frac{2}{21}$

Option 3: $\frac{4}{21}$

Option 4: $\frac{8}{21}$

Question : If $\theta$ is an acute angle and $\cos\theta=\frac{11}{17}$, what is the value of $\tan\theta$?

Option 1: $\frac{4 \sqrt{10}}{11}$

Option 2: $\frac{13}{11}$

Option 3: $\frac{2 \sqrt{42}}{11}$

Option 4: $\frac{2 \sqrt{42}}{17}$

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: $\sqrt{3}$