Question

Довести тотожність: cos4 a tg2 a - sin4 a = -tg a

Answer 1

$cos4 alpha tg2alpha -sin4alpha = dfrac{cos 4alpha sin2alpha -sin4alpha cos2alpha }{cos2alpha } =\ \ = dfrac{-sin(4alpha -2alpha )}{cos2alpha } =- dfrac{sin2alpha }{cos2alpha } =-tg2alpha$