Cos x - sin 4x = cos 3x

cos x - sin 4x = cos 3x

cos x - cos 3x - sin 4x = 0

2sin2xsinx - 2sin2xcos2x = 0

2sin2x (sinx-cos2x) = 0

sin2x=0

2x=pik

x=pik/2, k∈Z

sinx-cos2x=0

2sinx^2x+sinx-1=0

sinx=t

2t^2+t-1=0

D=9

t = (-1+3) / 4 = 1/2

t = (-1-3) / 4 = - 1

x = - pi/2+2pik, k∈Z

x = pi/6+2pik, k∈Z

x = 5pi/6+2pik, k∈Z