Question

2sin(x-pi/3)=-√3
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Answer 1

$2sinBig(x-dfrac{pi}3Big)=-sqrt3\\sinBig(x-dfrac{pi}3Big)=-dfrac{sqrt3}2\\\1)~x-dfrac{pi}3=-dfrac{pi}3+2pi n;~~~boxed{boldsymbol{x_1=2pi n,~n in mathbb Z}}\\\2)~x-dfrac{pi}3=-dfrac{2pi}3+2pi k;~~~boxed{boldsymbol{x_2=-dfrac {pi}3+2pi k,~k in mathbb Z}}$