20.5. sin 2x*sin 6x - cos 2x*cos 6x = √2*sin 3x*cos 8x
-(cos 2x*cos 6x - sin 2x*sin 6x) = √2*sin 3x*cos 8x
-cos (2x + 6x) = √2*sin 3x*cos 8x
1) cos 8x = 0;
8x1 = pi/2 + 2pi*k1; x1 = pi/16 + pi/4*k1
8x2 = 3pi/2 + 2pi*k2; x2 = 3pi/16 + pi/4*k2
2) √2*sin 3x = -1; sin 3x = -1/√2
3x3 = -pi/4 + 2pi*n1; x3 = -pi/12 + 2pi/3*n1
3x4 = 5pi/4 + 2pi*n2; x4 = 5pi/12 + 2pi/3*n2
20.6. sin(z/2)*cos(3z/2) - 1/√3*sin(2z) = sin(3z/2)*cos(z/2)
sin(z/2)*cos(3z/2) - cos(z/2)*sin(3z/2) = 1/√3*2sin z*cos z
sin(z/2 - 3z/2) = 1/√3*2sin z*cos z
-sin z = 2/√3*sin z*cos z
1) sin z = 0; z1 = pi*k
2) -1 = 2/√3*cos z
cos z = -√3/2
z2 = 5pi/6 + 2pi*n
z3 = 7pi/6 + 2pi*m