If cos⁡x=2cos⁡y−12−cos⁡y, where x,y∈(0,π), then tan⁡x2cot⁡y2 is equal to

cos⁡x=2cos⁡y−12−cos⁡y⇒ 1−tan2⁡x21+tan2⁡x2=21−tan2⁡y/21+tan2⁡y/2−12−1−tan2⁡y/21+tan2⁡y/2=1−3tan2⁡y21+3tan2⁡y2⇒ tan2⁡x2=3tan2⁡y2 or  tan⁡x2cot⁡y2=3 (∵x,y∈(0,π))