Question

завтра контрольная, хелп докажите справедливость равенства: 2sin(2a+pi/4)sin(2a-pi/4)=-cos4a

Answer 1

$2\sin(2\alpha+\frac{\pi}{4})\sin(2\alpha-\frac{\pi}{4})=2\sin(\frac{\pi}{2}+2\alpha-\frac{\pi}{4})\sin(2\alpha-\frac{\pi}{4})=\\ \\ \\ =2\cos(2\alpha-\frac{\pi}{4})\sin(2\alpha-\frac{\pi}{4})=\sin(4\alpha-\frac{\pi}{2})=-\cos4\alpha$