Question

cos(П/3+x)+cos(П/3-х)=0

Answer 1

cosπ/3cosx-sinπ/3sinx+cosπ/3cosx+sinπ/3sinx=0 ⇔ 
⇔ 1/2cosx-√3/2sinx+1/2cosx+√3/2sinx=0 ⇔ cosx=0 ⇔ x=+-π/2+2πn, n∈Z.