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If $\cos x + \cos y + \cos α = 0$ and $\sin x + \sin y + \sin α = 0$ then $\cot (\frac{x + y}{2})$ is equal to

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a

sin α

b

cos α

c

cot α

d

sin⁡x+y2

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detailed solution

Correct option is C

Given equations may be written ascos⁡x+cos⁡y=−cos⁡α and sin⁡x+sin⁡y=−sin⁡α⇒ 2cos⁡x+y2cos⁡x−y2=−cos⁡α----i and 2sin⁡x+y2cos⁡x−y2=−sin⁡α----iiFrom Eqs. (i) and (ii), we get2cos⁡x+y2cos⁡x−y22sin⁡x+y2cos⁡x−y2=cos⁡αsin⁡α⇒ cot⁡x+y2=cot⁡α

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