Question

Solve trig equation: 9 + cot^(2) x = 12

Answer 1

$9+\cot^2x=12$
$\cot^2x=3$
$\cot x=\pm\sqrt3$
$\tan x=\pm\dfrac1{\sqrt3}$

This happens on the unit circle whenever $x=\dfrac\pi6,\dfrac{5\pi}6,\dfrac{7\pi}6,\dfrac{11\pi}6$, and more generally for $x=\dfrac\pi6+n\pi$ and $x=-\dfrac\pi6+n\pi$ for integers $n$.