Докажите тождество sin(a-b)sin(a+b)=cos^2b-cos^2a

[latex]\sin( \alpha - \beta )\sin( \alpha + \beta )= \dfrac{\cos( \alpha - \beta - \alpha - \beta )-\cos( \alpha - \beta + \alpha + \beta )}{2} =\\ \\ = \dfrac{\cos2 \beta -\cos2 \alpha }{2} = \dfrac{2\cos^2 \beta -1-2\cos^2 \alpha +1}{2} =\cos^2 \beta -\cos^2 \alpha [/latex]