Question

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

Answer 1

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