Question : If $\cos\theta = \frac{x^2\:-\:y^2}{x^2\:+\:y^2}$, then the value of $\cot\theta$ is equal to:

Question : If $x\cos^{2}30^{\circ}\cdot \sin60^{\circ}=\frac{\tan^{2}45^{\circ}\cdot \sec60^{\circ}}{\operatorname{cosec}60^{\circ}}$, then the value of $x$ is:

Question : If ${\operatorname{cosec} 39^{\circ}} = x$, then the value of $ \frac{1}{\operatorname{cosec}^2 51^{\circ}} +\sin^239^{\circ} +\tan ^251^{\circ} -\frac{1}{\sin ^2 51^{\circ} \sec ^2 39^{\circ}}$ is:

Question : If $3 \sin x+4 \cos x=2$, then the value of $3 \cos x – 4 \sin x$ is equal to:

Question : In a $\triangle ABC, \angle B=\frac{\pi}{3}, \angle C=\frac{\pi}{4}$ and D divides BC internally in the ratio 1 : 3, then $\frac{\sin \angle BAD}{\sin \angle CAD}$ is equal to: