According to the trigonometric identities, we have that:
[tex]\begin{gathered} \sin x=\frac{1}{cscx} \\ \tan x=\frac{1}{cotx} \end{gathered}[/tex]
Substitute the expressions:
[tex]\frac{\sin x}{\tan^2x}=\frac{\frac{1}{cscx}}{(\frac{1}{cotx})2}[/tex]
Simplify:
[tex]=\frac{\frac{1}{cscx}}{\frac{1}{cot^2x}}[/tex]
Cross Multiplication:
[tex]=\frac{1\times cot^2x}{1\times cscx}=\frac{cot^2x}{cscx}[/tex]
