Решить уравнение 2cosx+3sinx=3

2cosx + 3sinx = 3

(2cosx + 3sinx) ^2 = 3^2

4cos^2x + 12cosx sinx + 9sin^2x = 9cos^2x + 9sin^2x

9sin^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 ∈Z

2) - 12sinx + 5cosx = 0

12sinx - 5cosx = 0 / : cosx ≠ 0

12tgx - 5 = 0

tgx = 5/12

x = arctg (5/12) + pik, k ∈Z