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 $\theta$ is an acute angle and $\cos\theta=\frac{11}{17}$, what is the value of $\tan\theta$?

Option 1: $\frac{4 \sqrt{10}}{11}$

Option 2: $\frac{13}{11}$

Option 3: $\frac{2 \sqrt{42}}{11}$

Option 4: $\frac{2 \sqrt{42}}{17}$

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 $\theta$ 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 $\theta$ is an acute angle and $\sin \theta \cos \theta=2 \cos ^3 \theta-\frac{1}{4} \cos \theta$, then the value of $\sin \theta$ is:

Option 1: $\frac{\sqrt{15}-1}{8}$

Option 2: $\frac{\sqrt{15}-1}{4}$

Option 3: $\frac{\sqrt{15}+1}{4}$

Option 4: $\frac{\sqrt{15}-1}{2}$