Question

If $\cos 3x=0$ and $x$ is acute, find the value of $({\cot }^{2}x-{\text{cosec}}^{2}x)$

Answer 1

$\cos 3x=0^{\circ }$
$\cos 3x=\cos {90}^{\circ }$
$3x={90}^{\circ }$
$x={30}^{\circ }$
Now, ${\cot }^{2}x-{\text{cosec}}^{2}x={\cot }^2{30}^{\circ }-{\text{cosec}}^2{30}^{\circ }$

$=(\sqrt{3}{)}^2-2^2=3-4=-1$

Answer:$-1$