**Proof.**We have seen here that \sin^2(x) + \cos^2(x) = 1. We can change that into the following:

\begin{align*} \sin^2(x) + \cos^2(x) = 1 &\iff \frac{1}{\sin^2(x)}(\sin^2(x) + \cos^2(x)) = \frac{1}{\sin^2(x)}\cdot 1 \\ &\iff \frac{\sin^2(x)}{\sin^2(x)} + \frac{\cos^2(x)}{\sin^2(x)} = \frac{1}{\sin^2(x)} \\ &\iff 1 + \frac{\cos^2(x)}{\sin^2(x)} = \frac{1}{\sin^2(x)}. \end{align*}

\begin{align*} 1 + \cot^2(x) = \csc^2(x). \end{align*}