Question

verify trig identity cot^2(x)/1-sin^2(x) =csc^2(x)

Answer 1

$\begin{gathered} \frac{\cot^2(x)}{1-\sin^2(x)}=\csc ^2(x) \\ \\ \cot ^2(x)=\frac{\cos ^2(x)}{\sin ^2(x)} \\ \\ 1-\sin ^2(x)=\cos ^2(x) \\ \text{Hence} \\ \frac{\frac{\cos^2(x)}{\sin^2(x)}}{\cos ^2(x)}=\csc ^2(x) \\ \\ \frac{\cos ^2(x)}{\sin ^2(x)\cos ^2(x)}=\csc ^2(x) \\ \\ \frac{1}{\sin ^2(x)}=\csc ^2(x) \\ \\ \csc ^2(x)=\csc ^2(x) \\ \text{The trig identity is true} \end{gathered}$