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 $\theta$ 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

Question : If 3 cot A = 4 and A is an acute angle, then find the value of sec A.

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

Option 2: $\frac{5}{4}$

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

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

Question : If $\theta$ is a positive acute angle and $4\cos ^{2}\theta -4\cos \theta +1=0$, then the value of $\tan (\theta -15^{\circ})$is equal to:

Option 1: $0$

Option 2: $1$

Option 3: $\sqrt{3}$

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

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: $4$