If sin⁡xsin⁡y=12,cos⁡xcos⁡y=32,where x,y∈0,π2, then the value of tan (x+y) is equal to

Given,sin⁡xsin⁡y=12, cos⁡xcos⁡y=32⇒ tan⁡xtan⁡y=13tan⁡(x+y)=tan⁡x+tan⁡y1−tan⁡xtan⁡y=4tan⁡x1−3tan2⁡x Also,  sin⁡y=2sin⁡x, cos⁡y=23cos⁡x⇒sin2⁡y+cos2⁡y=4sin2⁡x+4cos2⁡x9=1⇒ 36tan2⁡x+4=9sec2⁡x=91+tan2⁡x⇒ 27tan2⁡x=5⇒ tan⁡x=533⇒ tan⁡(x+y)=45331−1527=15