Question

$cos frac{ pi (x-2)}{3} = frac{1}{2}$

Answer 1

$cos frac{pi (x-2)}{3}=frac{1}{2}\\frac{pi (x-2)}{3}=pm frac{pi}{3}+2pi n ; ,; nin Z\\x-2=pm frac{pi}{3}cdot frac{3}{pi}+frac{6pi n}{pi }=pm 1+6n; ,; nin Z\\x=pm 1+2+6n= left [ {{3+6n=3(2n+1)} atop {1+6n; ,; nin Z}} right.$