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#3.3.
4sinx + 5cosx = 4

Сделаем замену tg(x/2) = t. Тогда sinx = 2t/(t²+1), cosx = (1-t²)/(t²+1)
8t/(t²+1) + 5(1-t²)/(t²+1) = 4
8t + 5 - 5t² = 4t² + 4
9t² - 8t - 1 = 0
t_1,2 = (8 ± √(64 + 36))/18; t₁ = 1, t₂ = -1/9

1. tg(x/2) = 1; x/2 = π/4 + πn, n є Z; x = π/2 + 2πn, n є Z
2. tg(x/2) = -1/9; x/2 = arctg(-1/9) + πn, n є Z; x = 2arctg(-1/9) + 2πn, n є Z