Question

2cos(x/3-p/6)=-корень из3

Answer 1

$2cosBig(dfrac x3-dfrac{pi}6Big)=-sqrt 3\ \ \cosBig(dfrac x3-dfrac{pi}6Big)=-dfrac{sqrt 3}2\ \ \1)~~dfrac x3-dfrac{pi}6=dfrac{5pi}6+2pi n\ \ \~~~~~dfrac x3=dfrac{pi}6+dfrac{5pi}6+2pi n\ \ \~~~~~dfrac x3=pi+2pi n\ \ boxed{boldsymbol{x_1=3pi+6pi n;~~nin Z}}\ \ \2)~~dfrac x3-dfrac{pi}6=-dfrac{5pi}6+2pi m\ \ \~~~~~dfrac x3=dfrac{pi}6-dfrac{5pi}6+2pi m\ \ \~~~~~dfrac x3=-dfrac{2pi}3+2pi m\ \ boxed{boldsymbol{x_2=-2pi+6pi m;~~min Z}}$