Question

If $\cos 3x=0$ and $x$ is acute, then find the value of:

$|{\cot }^{2}x+{\csc }^{2}x|$

Answer 1

$\cos 3x=0$
$\cos 3x=\cos 90$
$3x=90$
$x={30}^{\circ }$
$|{\cot }^{2}x+{\csc }^{2}x|$
= $|{\cot }^{2}30+{\csc }^{2}30|$
= $|(\sqrt{3}{)}^2+2^2|$
= $|3+4|$= $7$