Question

Доведіть тотожність,алгебра 10 клас

Answer 1

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

$= - \dfrac{\cos \alpha }{\sin \alpha } = -\text{ctg} \, \alpha$