If $\tan \theta = \frac{{x\,\sin \,\phi }}{{1 - x\,\cos \,\phi }}$ and $\tan \,\phi = \frac{{y\sin \,\theta }}{{1 - y\,\cos \,\theta }}$, then $\frac{x}{y} = $
$\frac{{\sin \phi }}{{\sin \theta }}$
$\frac{{\sin \theta }}{{\sin \phi }}$
$\frac{{\sin \phi }}{{1 - \cos \theta }}$
$\frac{{\sin \theta }}{{1 - \cos \phi }}$
Observe that, at any instant, the minute and hour hands of a clock make two angles between them whose sum is $360^{\circ}$. At $6: 15$ the difference between these two angles is $....^{\circ}$
Find the value of $\sin 15^{\circ}$
Prove the $\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]=1$
Prove that $\cos \left(\frac{3 \pi}{4}+x\right)-\cos \left(\frac{3 \pi}{4}-x\right)=-\sqrt{2} \sin x$