5-4 cos2 x = 5 sin2 x

5 - (4 - 8sin²x) = 10sinxcosx 1 + 8sin²x = 10sinxcosx 9sin²x + cos²x - 10sinxcosx = 0 9tg²x - 10tgx + 1 = 0 Пусть t = tgx. 9t² - 10t + 1 = 0 D = 100 - 36 = 64 = 8² t1 = (10 + 8)/18 = 1 t2 = (10 - 8)/18 = 2/18 = 1/9. Обратная замена: tgx = 1 x = π/4 + 2πn, n ∈ Z. tgx = 1/9 x = arctg(1/9) + πn, n ∈ Z.