0,5*2SinxCosx + Cos²x -(Cos²x - Sin²x) = 0,5(tgx +1)
SinxCosx +Cos²x -Cos²x +Sin²x = 0,5(Sinx/Cosx +1)
SinxCosx +Sin²x = 0,5*(Sinx +Cosx)/Cosx
Sinx(Cosx +Sinx ) - 0,5*(Sinx +Cosx)/Cosx=0
(Cosx +Sinx)(Sinx - 0,5/Сosx) = 0
Cosx +Sinx = 0|:Сosx ≠ 0 или Sinx -0,5/Cosx= 0|*Cosx ≠0, x≠π/2+πn
1 + tgx = 0 SinxCosx - 0,5 = 0 |*2
tgx = -1 2SinxCosx -1 = 0
x = -π/4 + πk , k ∈ Z Sin2x = 1
2x = π/2 + πm , m ∈Z
x = π/4 + πm/2, m ∈Z