2 sin во 2ст x +3 cos x = 0 помогите)!

Question

2 sin во 2ст x +3 cos x = 0 помогите)!

Answer 1

2sin²x+3cosx=0
2*(1-cos²x)+3cosx=0
-2cos²x+3cosx+2=0
cosx=t, t∈[-1;1]
2t²-3t-2=0
t₁=2, 2∉[-1;1]
t₂=-1/2

t=-1/2
cosx=-1/2
x=+-(arccos(-1/2))+2πn, n∈Z
x=+-(π-arccos(1/2))+2πn, n∈Z
x=+-(2π/3)+2πn, n∈Z