\(\sqrt{3}\cdot tan\left(x-60^0\right)=3\)
=>\(tan\left(x-60^0\right)=\dfrac{3}{\sqrt{3}}=\sqrt{3}\)
=>\(x-60^0=60^0+k\cdot180^0\)
=>\(x=120^0+k\cdot180^0\)
\(x\in\left(-120^0;360^0\right)\)
=>\(120^0+k\cdot180^0\in\left(-120^0;360^0\right)\)
=>\(k\cdot180^0\in\left(-240^0;240^0\right)\)
=>\(k\in\left(-\dfrac{4}{3};\dfrac{4}{3}\right)\)
mà k nguyên
nên \(k\in\left\{-1;0;1\right\}\)
=>\(x\in\left\{120^0;-60^0;300^0\right\}\)
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