Prove the identities

1. $$(\sin u-1{)}^2+(\cos u+1{)}^2=3-2(\sin u-\cos u)$$
2. $$(\sin t+\cos t-1)(\sin t+\cos t+1)=2\sin t\cos t$$
3. $$k+(k^2+1)\sin x\cos x=(k\cos x+\sin x)(k\sin x+\cos x)$$