Question

Докажите тождество, решите плизззз

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Answer 1

$\displaystyle \dfrac{\sin(\alpha-\beta)}{{\rm tg}\, \alpha-{\rm tg}\, \beta}-\dfrac{\sin(\alpha+\beta)}{{\rm ctg}\, \alpha+{\rm ctg}\, \beta}=\dfrac{\sin(\alpha-\beta)}{\dfrac{\sin(\alpha-\beta)}{\cos\alpha\cos \beta}}-\dfrac{\sin(\alpha+\beta)}{\dfrac{\sin(\alpha+\beta)}{\sin\alpha\sin\beta}}=\\ \\ \\ =\cos\alpha\cos \beta-\sin\alpha\sin\beta=\cos(\alpha+\beta)$