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