Cox^2x-3cosx×sinx+2sin^2x=0 Помогитеее прошу, срочно

Question

Cox^2x-3cosx×sinx+2sin^2x=0
Помогитеее прошу, срочно

Answer 1

Cos²x - 3CosxSinx + 2Sin²x =0
Разделим обе части на Cos²x≠0

tg²x - 3tgx + 2 = 0
tgx = m
m² -3m +2 = 0
D = (-3)² - 4*2 = 9-8=1
m₁ = (3+1)/2 = 2
m₂ = (3 - 1)/2 = 1
tgx =2                                          tgx = 1
x = arctg2 + πn, n ∈ z                 x = arctg1 + πn, n ∈ z
                                                    x = π/4 + πn, n ∈ z