If $\cos (\alpha - \beta ) = 1$ and $\cos (\alpha + \beta ) = \frac{1}{e}$, $ - \pi < \alpha ,\beta < \pi $, then total number of ordered pair of $(\alpha ,\beta )$ is

Find the degree measures corresponding to the following radian measures (Use $\pi=\frac{22}{7}$ ).

$\frac{5 \pi}{3}$

The value of $\tan ( - 945^\circ )$ is

$\cos 1^\circ + \cos 2^\circ + \cos 3^\circ + ..... + \cos 180^\circ = $

If the arcs of the same length in two circles $S_1$ and $S_2$ subtend angles $75^o $ and $120^o $ respectively at the centre. The ratio $\frac{{{S_1}}}{{{S_2}}}$ is equal to

If $x = \sec \theta + \tan \theta ,$ then $x + \frac{1}{x} = $