Question

доказать тождество 3cos 2α-sin^2α-cos^2α=2cos 2α

Answer 1

$3cos2 alpha -sin^2 alpha -cos^2 alpha =2cos2 alpha ,\\3(cos^2 alpha -sin^2 alpha )-sin^2 alpha -cos^2 alpha=3cos^2 alpha -3sin^2 alpha -sin^2 alpha -cos^2 alpha\=2cos^2alpha-2sin^2a=2(cos^2 alpha-sin^2alpha)=2cos2 alpha.\\2cos2alpha=2cos2alpha.$