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 $4 \sin ^2 \mathrm{A}-3=0$ and $0 \leq \mathrm{A} \leq 90^{\circ}$, then $3 \sin \mathrm{A}-4 \sin ^3 \mathrm{A}$ is:

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

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

Option 3: $0$

Option 4: $1$

Question : If $\theta$ is a positive acute angle and $4\cos ^{2}\theta -4\cos \theta +1=0$, then the value of $\tan (\theta -15^{\circ})$is equal to:

Option 1: $0$

Option 2: $1$

Option 3: $\sqrt{3}$

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

Question : If $(\sin \theta-\cos \theta)=0$, then the value of $\sin\;(\pi-\theta)+\sin \left(\frac{\pi}{2}-\theta\right)$ is:

Option 1: $1$

Option 2: $0$

Option 3: $\sqrt{3}$

Option 4: $\sqrt{2}$

Question : If $\frac{\sin \theta}{\cot \theta+\operatorname{cosec} \theta}=1$, then what is the value of $\theta$?

Option 1: $30^{\circ}$

Option 2: $90^{\circ}$

Option 3: $0^{\circ}$

Option 4: $45^{\circ}$