Question

Представьте в виде произведения выражение cosx+ cos2x+cos3x+cos4x

Answer 1

$\cos x+\cos3x+\cos2x+\cos4x= \\ =2\cos2x\cdot \cos x+2\cos3x\cdot \cos x= \\ =2\cos x(\cos2x+\cos3x)=2\cos x\cdot 2\cos \frac{5x}{2} \cdot\cos \frac{x}{2} =\boxed{4\cos x\cdot\cos \frac{5x}{2}\cdot\cos \frac{x}{2}}$

Answer 2

(cosx+cos4x)+(cos2x+cos3x)=2cos(5x/2)cos(3x/2)+2cos(5x/2)cos(x/2)=
=2cos(5x/2)(cos(3x/2)+cos(x/2))=4cos(5x/2)cosxcos(x/2)