решить уравнение cosX+cos3X=4cos2X

2cos2xcos (-x) = 4cos2x

cos2xcosx=2cos2x

cos2x (2-cosx) = 0

cos2x=0 или cosx=2

1-2sin^2x=0 пусто cos [-1:1]

sin^2x=1/2

sinx=sqrt2/2 или sinx = - sqrt2/2

x = (-1) ^n pi/4 + pik или x = (-1) ^n+1 pi/4 + pik

x = pi/4+2pik x=5pi/4+2pik

x = 3pi/4 + 2pik x=7pi/4+2pik