Решение
sin²x - (5/2)*2sinxcosx + 2*sin²x + 2cos²x = 0
3sin²x - 5sinxcosx + 2cos²x = 0 делим на cos²x ≠ 0
3tg²x - 5tgx + 2 = 0
tgx = t
3t² - 5t + 2 = 0
D = 25 - 4*3*2 = 1
t₁ = (5 - 1)/6
t₁ = 2/3
t₂ = (5 + 1)/6
t₂ = 1
1) tgx = 2/3
x₁ = arctg(2/3) + πk, k ∈ Z
2) tgx = 1
x₂ = π/4 + πn, n ∈ Z