Question : If $(r\cos \theta -\sqrt{3})^{2}+(r\sin \theta -1)^{2}=0$, then the value of $\frac{r\tan \theta +\sec \theta}{r\sec \theta +\tan\theta}$ is equal to:

Option 1: $\frac{4}{5}$

Option 2:

$\frac{5}{4}$

Option 3:

$\frac{\sqrt{3}}{4}$

Option 4:

$\frac{\sqrt{5}}{4}$

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 $\sin(A+B)=\sin A\cos B+\cos A \sin B$, then the value of $\sin75°$ is:

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

Option 2:

$\frac{\sqrt{2}+1}{2\sqrt{2}}$

Option 3:

$\frac{\sqrt{3}+1}{2\sqrt{2}}$

Option 4:

$\frac{\sqrt{3}+1}{2}$

Question : Which of the following is a value of $\theta$, when $\cos ^2 \theta-2+\cos \theta=0$?

Option 1: 60°

Option 2: 90°

Option 3: 30°

Option 4: 0°