Question

помогите решить уравнение 2sin(pi+x/2)+cos(3pi+x)=1

Answer 1

2cos(x/2)-cosx=1
2cos(x/2)-2cos²(x/2)+1=1
2cos(x/2)*(1-cos(x/2))=0
cos(x/2)=0⇒x/2=π/2+πn⇒x=π+2πn,n∈z
cos(x/2)=1⇒x/2=2πk⇒x=4πk,k∈z