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 =2\cdot cos45\cdot sin(45- \alpha )=\sqrt2sin(\frac{\pi}{4}- \alpha )[/latex]