Question : If $\sin 2\theta=\frac{\sqrt{3}}{2}$, then the value of $\sin 3\theta$ is equal to $(0^{\circ}\leq \theta\leq 90^{\circ})$:

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

Option 2: $1$

Option 3: $0$

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

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 $(4 \sin \theta+5 \cos \theta)=3$, 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 $\cos A+\sin A=\sqrt{2}\cos A$, then $\cos A-\sin A$ is equal to: (where $0^{\circ}< A< 90^{\circ}$)

Option 1: $\sqrt{2}\sin A$

Option 2: $2\sin A$

Option 3: $2\sqrt{\sin A}$

Option 4: $\sqrt{2\sin A}$

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: $30^{\circ}$