If $\cos x + \cos y + \cos \alpha = 0$ and $\sin x + \sin y + \sin \alpha = 0,$ then $\cot \,\left( {\frac{{x + y}}{2}} \right) = $
If $\cos x + \cos y + \cos \alpha = 0$ and $\sin x + \sin y + \sin \alpha = 0,$ then $\cot \,\left( {\frac{{x + y}}{2}} \right) = $
- A
$\sin \alpha $
- B
$\cos \alpha $
- C
$\cot \alpha $
- D
$\sin \,\left( {\frac{{x + y}}{2}} \right)$
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