Question

Trig I need to verify the identity for the equation in the pic #3

Answer 1

According to the trigonometric identities, we have that:

$\begin{gathered} \sin x=\frac{1}{cscx} \\ \tan x=\frac{1}{cotx} \end{gathered}$

Substitute the expressions:

$\frac{\sin x}{\tan^2x}=\frac{\frac{1}{cscx}}{(\frac{1}{cotx})2}$

Simplify:

$=\frac{\frac{1}{cscx}}{\frac{1}{cot^2x}}$

Cross Multiplication:

$=\frac{1\times cot^2x}{1\times cscx}=\frac{cot^2x}{cscx}$