Question

Докажите тождество, решите плизззз

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Answer 1

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