sin²x - 2sinxcosx - 3cos²x = 0 | : cos²x
tg²x - 2tgx - 3 = 0
Substitution : TGX = a
a² - 2a - 3 = 0
by t . vieta :
a₁ = 3
a₂ = -1
inverse substitution :
TGA = 3
x₁ = arctg3 + piN , n∈Z
TGA = -1
x₂ = -π / 4 + piN , n∈Z
On promežutke [ -π , π / 2 ] equation has two roots to -π / 4; arctg3