Cos2 L/ cos L + sin L

[latex] frac{cos2 alpha }{cos alpha +sin alpha } = frac{cos^2 alpha -sin^2 alpha }{cos alpha +sin alpha } =frac{(cos alpha -sin alpha )(cos alpha +sin alpha )}{cos alpha +sin alpha } =cos alpha -sin alpha =\\=sin(90- alpha )-sin alpha =2cdot cos45cdot sin(45- alpha )=sqrt2sin(frac{pi}{4}- alpha )[/latex]