sin^2x + 2sinxcosx - (cos^2x + sin^2x) = 0 sin^2x + 2sinxcosx - cos^2x - sin^2x = 0 cosx (2sinx - cosx) = 0 1) cosx =  0x = pi/2 + pik, k ∈Z2) 2sinx - cosx = 0   /:cosx≠ 02tgx - 1 = 0 tgx = 1/2x = arctg(1/2) + pik, k ∈Z

sin²x + sin2x = 1Разложим синус удвоенного аргумента:sin²x + 2sinxcosx - 1 = 0-(1 - sin²x) + 2sinxcosx = 0-cos²x + 2sinxcosx = 0cosx(-cosx + 2sinx) = 0cosx = 0x = π/2 + πn, n ∈ Zcosx = 2sinx1 = 2tgxtgx = 1/2x = arctg(1/2) + πn, n ∈ Z.