Question

transformati in produs cosx+cos2x+cos6x+cos7x

Answer 1

[tex]\text{Folosim aceeasi idee:}\\ \cos x+\cos 2x+\cos 6x+\cos 7x=(\cos 7x+\cos x)+(\cos6x+\cos 2x)=\\ =2\cos \dfrac{7x+x}{2}\cos \dfrac{7x-x}{2}+2\cos \dfrac{6x+2x}{2}\cos \dfrac{6x-2x}{2}= \\ =2\cos 4x\cdot \cos 3x +2\cos 4x\cdot \cos 2x=2\cos 4x(\cos 3x+\cos 2x)=\\ =calcule= 2\cos 4x\cdot \cos \dfrac{5x}{2}\cdot \cos \dfrac{x}{2}[/tex]