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

Option 1: $\frac{5}{12}$

Option 2: $\frac{12}{13}$

Option 3: $\frac{11}{12}$

Option 4: $\frac{5}{13}$

Question : If $\operatorname{sin} \theta=\frac{4}{5}$, find the value of $\tan \theta-\operatorname{cot} \theta$.

Option 1: $\frac{5}{12}$

Option 2: $\frac{7}{9}$

Option 3: $\frac{7}{12}$

Option 4: $\frac{7}{8}$

Question : Find the value of the following expression.
$5\left(\sin ^4 \theta+\cos ^4 \theta\right)+3\left(\sin ^6 \theta+\cos ^6 \theta\right)+19 \sin ^2 \theta \cos ^2 \theta$

Option 1: 8

Option 2: 5

Option 3: 6

Option 4: 7

Question : If $\frac{(3 \sin \theta-\cos \theta)}{(\cos \theta+\sin \theta)}=1$, then the value of $\cot \theta$ is:

Option 1: 3

Option 2: 0

Option 3: 1

Option 4: 2