Question : If $r=15(\sin \theta+\cos \theta)$ and $s=16(\sin \theta-\cos \theta)$, then the value of $\frac{r^2}{15^2}+\frac{s^2}{16^2}$ is:

Option 1: 8

Option 2: 6

Option 3: 4

Option 4: 2

Question : If $x=8(\sin \theta+\cos \theta)$ and $y=9(\sin \theta-\cos \theta)$, then the value of $\frac{x^2}{8^2}+\frac{y^2}{9^2}$ is:

Option 1: 4

Option 2: 6

Option 3: 8

Option 4: 2

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 $8 \cot \theta=6$, then the value of $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}$ is:

Option 1: 12

Option 2: 7

Option 3: 2

Option 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: $–3$