If sinxsiny=12,cosxcosy=32,where x,y∈0,π2, then the value of tan (x+y) is equal to
13
14
17
15
Given,sinxsiny=12, cosxcosy=32
⇒ tanxtany=13
tan(x+y)=tanx+tany1−tanxtany=4tanx1−3tan2x Also, siny=2sinx, cosy=23cosx
⇒sin2y+cos2y=4sin2x+4cos2x9=1⇒ 36tan2x+4=9sec2x=91+tan2x⇒ 27tan2x=5⇒ tanx=533⇒ tan(x+y)=45331−1527=15