Докажите тождество подробно cosx+cos2x+cos6x+cos7x=4cosx/2*cos5x/2*cos4x

Question

Докажите тождество подробно
cosx+cos2x+cos6x+cos7x=4cosx/2*cos5x/2*cos4x

Answer 1

докажите тождество подробно
cosx+cos2x+cos6x+cos7x=4cosx/2*cos5x/2*cos4x
Cosx+cos2x+cos6x+cos7x=(Cosx + Cos7x )+ (Cos2x + Cos6x) = 
= 2Cos4x Cos3x + 2Cos4x Cos2x = 2Cos4x(Cos3x + Cos2x) =
= 2Cos4x*2Cos5/2x Cosx/2 = 4Cos4xCos5/2x Cosx/2