$\frac{{\sin 3\theta + \sin 5\theta + \sin 7\theta + \sin 9\theta }}{{\cos 3\theta + \cos 5\theta + \cos 7\theta + \cos 9\theta }} = $
$\tan 3\theta $
$\cot 3\theta $
$\tan 6\theta $
$\cot 6\theta $
If $\alpha ,\,\,\beta ,\gamma ,\,\,\delta $ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$, then the value of $4\,\sin \frac{\alpha }{2} + 3\,\sin \frac{\beta }{2} + 2\,\sin \frac{\gamma }{2} + \sin \frac{\delta }{2}$ is equal to
The value of $\cos \,\frac{\pi }{7}\,\cos \,\frac{{2\pi }}{7}\,\cos \,\frac{{3\pi }}{7}$ is
$\frac{{\tan A + \sec A - 1}}{{\tan A - \sec A + 1}} = $
The value of $\frac{{\tan {{70}^o} - \tan {{20}^o}}}{{\tan {{50}^o}}} = $
Prove that $\sin ^{2} 6 x-\sin ^{2} 4 x=\sin 2 x \sin 10 x$