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 $\mathrm{A}=\cot 30^{\circ} \tan 60^{\circ}+\cot 60^{\circ} \tan 30^{\circ}$, then what is the value of A?

Option 1: $\frac{1}{ \sqrt{ 3}}$

Option 2: $\frac{10}{3}$

Option 3: $\frac{10}{ \sqrt{3}}$

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

Question : If $\sqrt{3} \tan ^2 \theta-4 \tan \theta+\sqrt{3}=0$, then what is the value of $\tan ^2 \theta+\cot ^2 \theta$?

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

Option 2: $\frac{10}{3}$

Option 3: $3$

Option 4: $\frac{6}{5}$

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 : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.

Option 1: $\frac{7}{6 \sqrt{3}}$

Option 2: $\frac{\sqrt{3}}{6}$

Option 3: $\frac{7}{6}$

Option 4: $\frac{7}{2 \sqrt{3}}$