Prove the identities

1. $$\tan x(1-{\sin }^{2}x)=\sin x\cos x$$
2. $$\frac{\sin y}{1-{\sin }^{2}y}=\frac{\tan y}{\cos y}$$
3. $$\sin u\tan u=\frac{1-{\cos }^{2}u}{\cos u}$$