Question

Решить уравнение 2cosx+3sinx=3

Answer 1

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