If cos⁡x+cos⁡y+cos⁡α=0 and sin⁡x+sin⁡y+sin⁡α=0 then cot⁡x+y2 is equal to

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