Question

Cos2x+cos4x упростить

Answer 1

$cos2x+cos4x=2cos\frac{4x+2x}{2}\cdot cos\frac{4x-2x}{2}=2cos3x\cdot cosx\\\\ili\\\\cos2x+cos4x=cos2x+(2cos^22x-1)=\\\\=2\cdot (cos2x+1)(cos2x-\frac{1}{2})\\\\\\P.S.\quad cos^2 \alpha = \frac{1+cos2 \alpha }{2} \; \; \Rightarrow \; \; cos2 \alpha =2cos^2 \alpha -1\\\\2t^2+t-1=2(t+1)(t-\frac{1}{2})$