Question : If $2 \cot \theta = 3$, find the value of $\frac{\sqrt{13} \sin \theta – 3 \tan \theta}{3 \tan \theta + \sqrt{13} \cos \theta}$

Question : If $\theta$ is a positive acute angle and $4\sin^{2}\theta =3$, then the value of $\left (\tan\theta-\cot\frac{\theta}{2}\right)$ is:

Question : Using $\cos (A+B)=\cos A \cos B-\sin A \sin B$, find the value of $\cos 75^\circ$.

Question : In $\triangle{XYZ}$, right-angled at $Y$, if $\sin X = \frac{1}{2}$, find the value of $\cos X \cos Z + \sin X \sin Z$.

Question : Find the value of $\frac{\cos^2 15^{\circ}-\sin^2 15^{\circ}}{\cos^2 145^{\circ}+\sin^2 145^{\circ}}$.