Prove the $\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]=1$
$L.H.S.$ $=\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]$
$=\sin x \cos x[\tan x+\cot x]$
$=\sin x \cos x\left(\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}\right)$
$=(\sin x \cos x)\left[\frac{\sin ^{2} x+\cos ^{2} x}{\sin x \cos x}\right]$
$=1= R. H. S.$
Find the radian measures corresponding to the following degree measures:
$520^{\circ}$
At what time between $10\,\,O'clock$ and $11\,\,O 'clock$ are the two hands of a clock symmetric with respect to the vertical line (give the answer to the nearest second)?
Find the values of other five trigonometric functions if $\cos x=-\frac{1}{2}, x$ lies in third quadrant.
The value of $\cos A - \sin A$ when $A = \frac{{5\pi }}{4},$ is