Упростить:

Решите задачу:

$\cos( \alpha - \beta )-\cos( \alpha + \beta )=\cos \alpha \cos \beta +\sin \alpha \sin \beta -\cos \alpha \cos \beta +\\+\sin \alpha \sin \beta =2\sin \alpha \sin \beta$

$\frac{\sin(- \alpha )+\cos( \pi + \alpha )}{1+2\cos( \frac{\pi}{2}- \alpha )\cos(- \alpha ) } = \frac{-\sin \alpha -\cos \alpha }{1+2\sin \alpha \cos \alpha } = \frac{-(\sin \alpha +\cos \alpha )}{(\sin \alpha +\cos \alpha )^2} =- \frac{1}{\sin \alpha +\cos \alpha }$

$\sin5x\cos 4x-\cos 5x\sin 4x=\sin(5x-4x)=\sin x$