Cos4x+cos8x+cos12x=0

Question

Cos4x+cos8x+cos12x=0

Answer 1

cos4x+cos12x=2*cos 8x*cos 4x
Cos4x+cos8x+cos12x=2*cos 8x*cos 4x+cos 8x = 0
cos8x*(2cos4x+1)=0
cos8x=0 или cos4x = -1/28х = pi/2+pi*k или 4х = 2pi/3+2*pi*n или 4х = 4pi/3+2*pi*m
х = pi/16+pi/8 * k или х = pi/6+pi/2*n или х = pi/3+pi/2*m