Verified answer

sin((π/2)-x)=cosx

cos(π-x)=-cosx

sin(п/2-x)-cos(п-x)=cosx-(-cosx)=2cosx

2cosx=1

cosx=1/2

x=±arccos(1/2)+2πn, n∈Z

x=±(π/3)+2πn, n∈Z