Question

Решите уравнение.3*sin^2(x)-2*sin(x)*cos(x)-cos^2(x)=0

Answer 1

3sin²x - 2sinxcosx - cos²x = 0 делим на cos²x ≠ 0
3tg²x - 2tgx - 1 = 0
D = 4 + 4*3*1 = 16
1)  tgx = (2 - 4)/6
tgx = - 1/3
x₁ = - arctg(1/3) + πk, k∈Z
2)  tgx = (2 + 4)/6
tgx = 1
x₂ = π/4 + πn, n∈Z