4sin2x + 10cos²x = 1
8sinxcosx + 10cos²x = sin²x + cos²x
sin²x - 8sinxcosx - 9cos²x = 0 |:cos²x
tg²x - 8tgx - 9 = 0
tg²x - 8tgx + 16 - 25 = 0
(tgx - 4)² - 5² = 0
(tgx - 4 - 1)(tgx - 4 + 5) = 0
(tgx - 5)(tgx + 1) = 0
tgx = 5 или tgx = -1
x = arctg5 + πn, n ∈ Z
x = -π/4 + πn, n ∈ Z
Ответ: x = arctg5 + πn, n ∈ Z; x = -π/4 + πn, n ∈ Z.