Sinx + 2sinxcosx - cosx - 2cos^2x = 0
sinx (1 +2cosx) - cosx(1 + 2cosx) = 0
(sinx - cosx)*(1 + 2cosx) = 0
1) sinx - cosx = 0 /: cosx ≠ 0
tgx - 1 = 0
tgx = 1
x = pi/4 + pik, k ∈ Z
2) 1 + 2cosx = 0
2cosx = - 1
cosx = - 1/2
x = ± arccos(-1/2) + 2pik
x = ± 2pi/3 + 2pik, k ∈Z