Answer
\[\begin{gathered}
{\text{1)}}\,\,\,\,\,\,{\sin ^2}\theta + {\cos ^2}\theta = 1 \hfill \\
{\text{2)}}\,\,\,\,\,\,1 + {\cot ^2}\theta = {\csc ^2}\theta \hfill \\
{\text{3)}}\,\,\,\,\,\,{\tan ^2}\theta + 1 = {\sec ^2}\theta \hfill \\
\end{gathered} \]
Work Step by Step
\[\begin{gathered}
{\text{The three Pythagorean identities are:}}\,\,\,\left( {{\text{See page 41}}} \right) \hfill \\
{\text{1)}}\,\,\,\,\,\,{\sin ^2}\theta + {\cos ^2}\theta = 1 \hfill \\
{\text{2)}}\,\,\,\,\,\,1 + {\cot ^2}\theta = {\csc ^2}\theta \hfill \\
{\text{3)}}\,\,\,\,\,\,{\tan ^2}\theta + 1 = {\sec ^2}\theta \hfill \\
\end{gathered} \]
