[Math] How to prove $\cot ^2x+\sec ^2x=\tan ^2x+\csc ^2x$

Question

How can I prove the following equation?

\begin{eqnarray}
\cot ^2x+\sec ^2x &=& \tan ^2x+\csc ^2x\\
{{1}\over{\tan^2x}}+{{1}\over{\cos^2x}} &=& {{\sin^2x}\over{\cos^2x}}+{{1}\over{\sin^2x}}\\
{{\sin^2x+\cos^4x}\over{\sin^2x\cos^2x}} &=& {{\sin^4x+\cos^2x}\over{\sin^2x\ \cos^2x}}\\
\end{eqnarray}

Then, what can I do…?

Thank you for your attention.

Answer 1

HINT:

We know, $$\csc^2x-\cot^2x=1=\sec^2x-\tan^2x$$