Cos(x/5-п/3)=корень из 2/2

Question

Cos(x/5-п/3)=корень из 2/2

Answer 1

Cos(x/5-π/3)=(√2)/2⇒x1/5-π/3=0,25*π+2*π*n⇒0,2*x1=0,25*π+2*π*n+π/3⇒x1=2,5*π+10*π*n+5*π/3=14*π/3+10*π*n.
x2/5-π/3=7*π/4+2*π*n⇒0,2*x2=7*π/4+2*π*n+π/3⇒x2=35*π/4+10*π*n+5*π/3=125*π/12+10*π*n. n∈Z.

Ответ: х1=14*π/3+10*π*n; х2=125*π/12+10*π*n. n∈Z.