[tex]\bf \cfrac{tan(x)-cot(x)}{sin(x)cos(x)}\implies \cfrac{\frac{sin(x)}{cos(x)}-\frac{cos(x)}{sin(x)}}{sin(x)cos(x)}\implies \cfrac{\frac{sin^2(x)-cos^2(x)}{cos(x)sin(x)}}{\frac{sin(x)cos(x)}{1}}
\\\\\\
\cfrac{sin^2(x)-cos^2(x)}{cos(x)sin(x)}\cdot \cfrac{1}{sin(x)cos(x)}\implies \cfrac{sin^2(x)-cos^2(x)}{cos^2(x)sin^2(x)}
\\\\\\
\textit{and now, we distribute the denominator}
\\\\\\
\cfrac{sin^2(x)}{cos^2(x)sin^2(x)}-\cfrac{cos^2(x)}{cos^2(x)sin^2(x)}\implies
\cfrac{1}{cos^2(x)}-\cfrac{1}{sin^2(x)}[/tex]
and surely you know what that is
