Question

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

Answer 1

$2sin(2alpha+frac{pi}{4})sin(2alpha-frac{pi}{4})=2sin(frac{pi}{2}+2alpha-frac{pi}{4})sin(2alpha-frac{pi}{4})=\ \ \ =2cos(2alpha-frac{pi}{4})sin(2alpha-frac{pi}{4})=sin(4alpha-frac{pi}{2})=-cos4alpha$