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