7sin^2x=8sinxcosx-cos^2xСРОЧНЯК ПРЯМ НАДОРЕБЯЯТ

Решение 7sin^2x=8sinxcosx-cos^2x 7sin^2x - 8sinxcosx + cos^2x = 0 делим на cos²x ≠ 0 7tg²x - 8tgx + 1 = 0 tgx = t 7t² - 8t + 1 = 0 D = 64 - 4*7*1 = 36 t = (8 - 6)/14 = - 1/7 t = (8 + 6)/14 = 1 1)  tgx = - 1/7 x₁ = - arctg(1/7) + πk, k ∈ Z 2) tgx = 1 x₂ = π/4 + πn, n ∈Z Ответ: x₁ = - arctg(1/7) + πk, k ∈ Z ; x₂ = π/4 + πn, n ∈Z