$\frac{{\tan A + \sec A - 1}}{{\tan A - \sec A + 1}} = $
$\frac{{1 - \sin A}}{{\cos A}}$
$\frac{{1 - \cos A}}{{\sin A}}$
$\frac{{1 + \sin A}}{{\cos A}}$
$\frac{{1 + \cos A}}{{\sin A}}$
${\sin ^2}\frac{\pi }{8} + {\sin ^2}\frac{{3\pi }}{8} + {\sin ^2}\frac{{5\pi }}{8} + {\sin ^2}\frac{{7\pi }}{8} = $
Prove that $\tan 4 x=\frac{4 \tan x\left(1-\tan ^{2} x\right)}{1-6 \tan ^{2} x+\tan ^{4} x}$
$\frac{{\cos 12^\circ - \sin 12^\circ }}{{\cos 12^\circ + \sin 12^\circ }} + \frac{{\sin 147^\circ }}{{\cos 147^\circ }} = $
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
If ${\rm{cosec}}\theta = \frac{{p + q}}{{p - q}},$ then $\cot \,\left( {\frac{\pi }{4} + \frac{\theta }{2}} \right) = $