[tex]\bf 1+tan^2(\theta)=sec^2(\theta)\qquad \qquad sin(-\theta )=-sin(\theta )
\\\\\\
cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\qquad \qquad csc(\theta)=\cfrac{1}{sin(\theta)}
\qquad \qquad
% secant
sec(\theta)=\cfrac{1}{cos(\theta)}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \cfrac{csc(-x)}{1+tan^2(x)} \implies \cfrac{csc(-x)}{sec^2(x)}\implies \cfrac{\frac{1}{sin(-x)}}{\frac{1^2}{cos^2(x)}}
\\\\\\
\cfrac{1}{-sin(x)}\cdot \cfrac{cos^2(x)}{1}\implies -\cfrac{cos^2(x)}{sin(x)}\implies cos(x)\cfrac{cos(x)}{sin(x)}
\\\\\\
\boxed{cos(x)cot(x)}[/tex]
