20.1. cos 3x - sin x = √3*(cos x - sin 3x)
cos 3x + √3*sin 3x = sin x + √3*cos x
2*(1/2*cos 3x + √3/2*sin 3x) = 2*(1/2*sin x + √3/2*cos x)
sin(pi/6)*cos 3x + cos(pi/6)*sin 3x = cos(pi/3)*sin x + sin(pi/3)*cos x
sin (pi/6 + 3x) = sin(pi/3 + x)
sin (pi/6 + 3x) - sin(pi/3 + x) = 0
2sin ((pi/6 + 3x - pi/3 - x)/2)*cos ((pi/6 + 3x + pi/3 + x)/2) = 0
sin ((2x - pi/6)/2)*cos ((4x + pi/2)/2) = 0
sin (x - pi/12)*cos (2x + pi/4) = 0
1) x - pi/12 = pi*k; x1 = pi/12 + pi*k
2) 2x + pi/4 = pi/2 + 2pi*n; x2 = pi/8 + pi*n
3) 2x + pi/4 = 3pi/2 + 2pi*m; x3 = 5pi/8 + pi*m
20.2. sin 3z - cos 3z = √(3/2)
√2*(1/√2*sin 3z - 1/√2*cos 3z) = √(3/2)
√2*(sin 3z*cos pi/4 - cos 3z*sin pi/4) = √(3/2)
√2*sin (3z - pi/4) = √3/√2
sin (3z - pi/4) = √3/2
1) 3z - pi/4 = pi/3 + 2pi*k; 3z = 7pi/12 + 2pi*k; z1 = 7pi/36 + 2pi/3*k
2) 3z - pi/4 = 2pi/3 + 2pi*n; 3z = 11pi/12 + 2pi*n; z2 = 11pi/36 + 2pi/3*n