Question

cos2x+cos4x упростить

Answer 1

$cos2x+cos4x=2cosfrac{4x+2x}{2}cdot cosfrac{4x-2x}{2}=2cos3xcdot cosx\\ili\\cos2x+cos4x=cos2x+(2cos^22x-1)=\\=2cdot (cos2x+1)(cos2x-frac{1}{2})\\\P.S.quad cos^2 alpha = frac{1+cos2 alpha }{2} ; ; Rightarrow ; ; cos2 alpha =2cos^2 alpha -1\\2t^2+t-1=2(t+1)(t-frac{1}{2})$