Спростите: Sinα*sin(α+β)+cosα*cos(α+β)

Решите задачу:

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