Question : If $\alpha$ is an acute angle and $2\sin \alpha+15\cos^2\alpha=7$, then the value of $\cot \alpha$ is:

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

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

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

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

Question : If $\sin \theta+\cos \theta=\frac{\sqrt{11}}{3}$, then the value of $(\cos \theta-\sin \theta)$ is:

Option 1: $\frac{\sqrt{5}}{3}$

Option 2: $\frac{7}{3}$

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

Option 4: $\frac{\sqrt{7}}{3}$

Question : If $\cos \theta+\sec \theta=2$, then the value of $\sin ^6 \theta+\cos ^6 \theta$ is:

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

Option 2: $0$

Option 3: $1$

Option 4: $\frac{1}{2}$

Question : If $\sin \theta+\cos \theta=\frac{\sqrt{11}}{3}$, then what is $\sin \theta-\cos \theta$?

Option 1: $\frac{\sqrt{7}}{4}$

Option 2: $\frac{\sqrt{7}}{3}$

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

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

Question : If $x=\frac{2 \sin \theta}{(1+\cos \theta+\sin \theta)}$, then the value of $\frac{1-\cos \theta+\sin \theta}{(1+\sin \theta)}$ is:

Option 1: $\frac{x}{(1+x)}$

Option 2: $x$

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

Option 4: $\frac{(1+x)}{x}$