This identity has been expressed wrongly because there is no divide sign. If y=45°, and tan(45)=sin(90)=1, so the identity would be:
LHS: sin(90)/(1+tan2(45))=½; RHS: 2tan(45)=2 and the identity is false because ½≠2.
But sin(90)(1+tan2(45))=2 so LHS=RHS. Now here's the proof:
sin(2y)=2sin(y)cos(y); 1+tan2(y)=sec2(y)=1/cos2(y).
So sin(2y)(1+tan2(y))=2sin(y)cos(y)/cos2(y)=2sin(y)/cos(y)=2tan(y) QED.