6(sin(x) + cos(x)) - sin(2x) + 6 = 0
6(sin(x) + cos(x) + 1) - sin(2x) = 0
6(sin(x) + 2cos^2(x/2)) - sin(2x) = 0
6sin(x) + 12cos^2(x/2) - 2sin(x)cos(x) = 0
3sin(x) - sin(x)cos(x) + 6cos^2(x/2) = 0
sin(x)(3 - cox(x)) + 6cos^2(x/2) = 0
sin(x)(2 + 2sin^2(x/2)) + 6cos^2(x/2) = 0
sin(x)(1 + sin^2(x/2)) + 3cos^2(x/2) = 0
sin(x)cos^2(x/2) + 3cos^2(x/2) = 0
cos^2(x/2)(sin(x) + 3) = 0
Данное равенство будет обращаться в 0, только когда
cos^2(x/2) = 0
cos(x/2) = 0
x/2 = p/2 + pk
x = p + 2pk, k E Z