20sin^3(x) + 3cosx = 3cos(3x) + 4sinx
20sin^3(x) - 4sinx = 3cos(3x) - 3cos(x)
20sin^3(x) - 4sinx = 3*(cos(3x) - cosx)
20sin^3(x) - 4sinx = 3*(-2*sin(2x)*sinx)
20sin^3(x) - 4sinx + 6sinx*sin(2x) = 0
10sin^3(x) - 2sinx + 3sinx*sin(2x) = 0
sin(x)*(10*sin^2(x) - 2 + 3sin(2x)) = 0
1) sinx = 0, x=πk
2) 10sin^2(x) - 2sin^2(x) - 2cos^2(x) + 6sinx*cosx = 0
8sin^2(x) + 6sinx*cosx - 2cos^2(x) = 0 - делим обе части на (2cos^2(x))
4tg^2(x) + 3tg(x) - 1 = 0
D = 9 + 4*4 = 25
tg(x) = 1/4, x=arctg(1/4) + πk
tg(x) = -1, x=-π/4 + πk