Question : If $\cos (3 \alpha)=\sin \left(\alpha-22^{\circ}\right)$, where $3 \alpha<90^{\circ}$, then what is the value of $\alpha$?

Option 1: 29°

Option 2: 26°

Option 3: 27°

Option 4: 28°

Question : If $\sin \alpha=\frac12$ and $\sin \beta=\frac12$, then what is the value of $\cos (\alpha+\beta)$? $(0°<\alpha, \beta<90° )$

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

Option 2: $\frac{1}{ 4}$

Option 3: $\frac12$

Option 4: $1$

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 $\cos 5 \alpha=\sin \alpha$ and $5 \alpha<90^{\circ}$, then the value of $\tan 2 \alpha$ is:

Option 1: $\sqrt{2}$

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

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

Option 4: $\sqrt{3}$

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

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

Option 2: $0$

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

Option 4: $1$