5-4 cos2 x = 5 sin2 x

5 - (4 - 8sin²x) = 10sinxcosx1 + 8sin²x = 10sinxcosx9sin²x + cos²x - 10sinxcosx = 09tg²x - 10tgx + 1 = 0Пусть t = tgx.9t² - 10t + 1 = 0D = 100 - 36 = 64 = 8²t1 = (10 + 8)/18 = 1t2 = (10 - 8)/18 = 2/18 = 1/9.Обратная замена:tgx = 1x = π/4 + 2πn, n ∈ Z.tgx = 1/9x = arctg(1/9) + πn, n ∈ Z.