Question

Докажите тождество
$4 sin alpha cos^3 alpha - 2sin2 alpha sin^2 alpha =sin4 alpha$

Answer 1

4sinαcos³α-2sin2αsin²α=4sinαcosαcos²α-2sin2αsin²α=
=2sin2αcos²α-2sin2αsin²α=2sin2α(cos²α-sin²α)=
=2sin2αcos2α=sin4α

( sin2α=2sinαcosα, cos2α=cos²α-sin²α)