1)
[tex]\bf \cfrac{cot(x)}{sin^2(x)}=\cfrac{csc^2(x)}{tan(x)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~\frac{cos(x)}{sin(x)}~~}{\frac{sin^2(x)}{1}}\implies \cfrac{cos(x)}{sin(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{cos(x)}{sin^3(x)}~\hfill \textit{doing the left-hand-side} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~\frac{1}{sin^2(x)}~~}{\frac{sin(x)}{cos(x)}}\implies \cfrac{1}{sin^2(x)}\cdot \cfrac{cos(x)}{sin(x)}\implies \cfrac{cos(x)}{sin^3(x)}~\hfill \textit{doing the right-hand-side}[/tex]
2)
[tex]\bf \cfrac{cos^2(x)+tan(x)}{sec(x)}=cos^3(x)+sin(x) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~cos^2(x)+\frac{sin(x)}{cos(x)}~~}{\frac{1}{cos(x)}}\implies \cfrac{~~\frac{cos^3(x)+sin(x)}{cos(x)}~~}{\frac{1}{cos(x)}}~\hfill \textit{doing the left-hand side} \\\\\\ \cfrac{cos^3(x)+sin(x)}{\underline{cos(x)}}\cdot \cfrac{\underline{cos(x)}}{1}\implies cos^3(x)+sin(x)[/tex]
