Question

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

Answer 1

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