Решить уравнение 2cosx+3sinx=3

2cosx + 3sinx = 3(2cosx + 3sinx)^2 = 3^24cos^2x + 12cosx sinx + 9sin^2x = 9cos^2x + 9sin^2x9sin^2x + 12cosx sinx + 4cos^2x - 9cos^2x - 9sin^2x = 0 - 5cos^2x + 12cosx sinx = 0 5cos^2x - 12cosx sinx = 0 cosx (5cosx - 12 sinx) = 0 1) cosx = 0 x = pi/2 + pik, k ∈Z2) - 12sinx + 5cosx = 0 12sinx - 5cosx = 0   /:cosx ≠ 0 12tgx - 5 = 0 tgx = 5/12x = arctg (5/12) + pik, k ∈Z