If $\sin \theta + \cos \theta = m$ and $\sec \theta + {\rm{cosec}}\theta = n$, then $n(m + 1)(m - 1) = $
$m$
$n$
$2m$
$2n$
Find $\sin \frac{x}{2}, \cos \frac{x}{2}$ and $\tan \frac{x}{2},$ if $\tan x=\frac{-4}{3}, x$ in quadrant $II$
If $\sin (\alpha - \beta ) = \frac{1}{2}$ and $\cos (\alpha + \beta ) = \frac{1}{2},$ where $\alpha $ and $\beta $ are positive acute angles, then
$\cos 1^\circ + \cos 2^\circ + \cos 3^\circ + ..... + \cos 180^\circ = $
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 $....^{\circ}$
If the arcs of the same lengths in two circles subtend angles $65^{\circ}$ and $110^{\circ}$ at the centre, find the ratio of their radii.