If $\sin (\alpha - \beta ) = \frac{1}{2}$ and $\cos (\alpha + \beta ) = \frac{1}{2},$ where $\alpha $ and $\beta $ are positive acute angles, then
$\alpha = 45^\circ ,\beta = 15^\circ $
$\alpha = 15^\circ ,\beta = 45^\circ $
$\alpha = 60^\circ ,\beta = 15^\circ $
None of these
Prove that:
$ 2 \cos \frac{\pi}{13} \cos \frac{9 \pi}{13}+\cos \frac{3 \pi}{13}+\cos \frac{5 \pi}{13}=0$
$(m + 2)\sin \theta + (2m - 1)\cos \theta = 2m + 1,$ if
$\cos 1^\circ + \cos 2^\circ + \cos 3^\circ + ..... + \cos 180^\circ = $
If $A + C = B,$ then $\tan A\,\tan B\,\tan C = $
Find the value of $\cos \left(-1710^{\circ}\right)$.