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 $\sin (\theta +18^{\circ})=\cos 60^{\circ}(0< \theta < 90^{\circ})$, then the value of $\cos 5\theta$ is:

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

Option 2: $0$

Option 3: $\frac{1}{\sqrt{2}}$

Option 4: $1$

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: $30^{\circ}$

Question : If $4\sin^{2}\theta-1=0$ and angle $\theta$ is less then $90^{\circ}$, the value of $\cos^{2}\theta+\tan^{2}\theta$ is:
(Take $0^{\circ}< \theta< 90^{\circ}$)

Option 1: $\frac{17}{15}$

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

Option 3: $\frac{11}{9}$

Option 4: $\frac{12}{11}$