2cos^2x*(-П/2-x)+sqrt(3)*sin2x=0

Question

2cos^2x*(-П/2-x)+sqrt(3)*sin2x=0

Answer 1

2cos²x(-(π/2+x)+√3sin2x=0
2sin²x+2√3sinxcosx=0
2sinx(sinx+√3cosx)=0
1) 2sinx=0
sinx=0
x=πn
2) sinx+√3cosx=0 |·1/2
1/2·sinx+√3/2·cosx=0
cosπ/3·six+sinπ/3·cosx=0
sin(π/3+x)=0
π/3+x=πn, n∈Z
x=πn-π/3, n∈Z