Question

Cosx+cos3x=cos2x решите плиз

Answer 1

$cos x+cos 3x=cos 2x \ 2cos frac{x+3x}{2} cdot cos frac{3x-x}{2} =cos 2x \ 2cos 2xcdot cos x=cos 2x \ 2cos2xcdot cos x-cos 2x=0 \ cos 2x(2cos x-1)=0 \ left[begin{array}{ccc}cos 2x=0\cos x= frac{1}{2} end{array}rightto left[begin{array}{ccc}x_1= frac{ pi }{4}+ frac{ pi n}{2} , n in Z\x_2=pm frac{ pi }{3}+2 pi n, n in Z end{array}right$