Question

Доказать тождество

cos3a/ cosa - sin3a/sina = -2

помогите пожалуйста 

Answer 1

$frac{cos3alpha}{cosalpha}-frac{sin3alpha}{sinalpha}=-2\sin3alpha=3sinalpha-4sin^3alphaquadquadcos3alpha=4cos^3alpha-3cosalpha\frac{cos3alpha}{cosalpha}-frac{sin3alpha}{sinalpha}=frac{4cos^3alpha-3cosalpha}{cosalpha}-frac{3sinalpha-4sin^3alpha}{sinalpha}=\=frac{cosalpha(4cos^2alpha-3)}{cosalpha}-frac{sinalpha(3-4sin^2alpha)}{sinalpha}=4cos^2alpha-3-3+4sin^2alpha=\=4(sin^2alpha+cos^2alpha)-6=4-6=-2$

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