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

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

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

Option 3: $3$

Option 4: $–3$

Question : If $\sin\theta+\sin^{2}\theta=1$, then the value of $\cos^{12}\theta+3\cos^{10}\theta+3\cos^{8}\theta+\cos^{6}\theta-1$ is:

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 0

Question : If $2 \cot \theta = 3$, find the value of $\frac{\sqrt{13} \sin \theta – 3 \tan \theta}{3 \tan \theta + \sqrt{13} \cos \theta}$

Option 1: $\frac{1}{\sqrt{13}}$

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

Option 3: 0

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

Question : If $\sin \theta=\frac{1}{2}$, then the value of $\left(3 \cos \theta-4 \cos ^3 \theta\right)$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: – 1