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
If $0 < x < \pi $ and $\cos x + \sin x = \frac{1}{2}$,then $tan \,x$ is
Prove the $\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]=1$
If $A$ lies in the second quadrant and $3\tan A + 4 = 0,$ the value of $2\cot A - 5\cos A + \sin A$ is equal to
$\cos 1^\circ .\cos 2^\circ .\cos 3^\circ .........\cos 179^\circ = $