Question

cos (x)/3sin (x)=1/ctg(x)

Answer 1

$\dfrac{\cos x}{3\sin x}=\dfrac{1}{\cot x}\\ \dfrac{1}{3}\cot x=\dfrac{1}{\cot x}\\ \cot^2 x=3\\ \cot x=-\sqrt3 \vee \cot x=\sqrt3\\ \boxed{x=-\dfrac{\pi}{6}+k\pi \vee x=\dfrac{\pi}{6}+k\pi, (k\in\mathbb{Z})}$