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