cosx + 3sin(x/2) = -1

Question

cosx + 3sin(x/2) = -1

Answer 1

Cosx+3sinx/2=-1
3*√(1-cosx)/2=-(cosx+1)
(1-cosx)/2=(cos²x+2cosx+1)/9
9-9cosx=2cos²x+4cosx+2
2cos²x+13cosx-7=0
cosx=a
2a²+13a-7=0
D=225
a1=(-13+15)/4=1/2 cosx=1/2 x=+-π/3+2πk
a2=(-13-15)/4=-7 нету решение