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

Option 1: $\frac{2}{5}$

Option 2: $\frac{1}{5}$

Option 3: $\frac{16}{25}$

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

Question : If $(4 \sin \theta+5 \cos \theta)=3$, then the value of $(4 \cos \theta-5 \sin \theta)$ is:

Option 1: $3 \sqrt{2}$

Option 2: $4 \sqrt{2}$

Option 3: $2 \sqrt{3}$

Option 4: $2 \sqrt{5}$

Question : If $0^{\circ} < \theta < 90^{\circ}$ and $2 \sin^{2}\theta +3\cos\theta =3$, then the value of $\theta$ is:

Option 1: 30°

Option 2: 60°

Option 3: 45°

Option 4: 75°

Question : If $\frac{\cos \theta}{(1+\sin \theta)}+\frac{\cos \theta}{(1-\sin \theta)}=4$ and $\theta$ is acute, then the value of $\theta$ is:

Option 1: $60^{\circ}$

Option 2: $15^{\circ}$

Option 3: $45^{\circ}$

Option 4: $30^{\circ}$

Question : If $\theta$ is an acute angle and $\sin \theta \cos \theta=2 \cos ^3 \theta-\frac{1}{4} \cos \theta$, then the value of $\sin \theta$ is:

Option 1: $\frac{\sqrt{15}-1}{8}$

Option 2: $\frac{\sqrt{15}-1}{4}$

Option 3: $\frac{\sqrt{15}+1}{4}$

Option 4: $\frac{\sqrt{15}-1}{2}$