Answer
$$\eqalign{
& \left. 1 \right)\,\,\,\,{\text{si}}{{\text{n}}^2}x + {\cos ^2}x = 1 \cr
& \left. 2 \right)\,\,\,1 + {\tan ^2}x = {\sec ^2}x \cr
& \left. 3 \right)\,\,\,{\cot ^2}x + 1 = {\csc ^2}x \cr} $$
Work Step by Step
$$\eqalign{
& {\text{The three Pythagorean identities are:}} \cr
& \left. 1 \right)\,\,\,\,{\text{si}}{{\text{n}}^2}x + {\cos ^2}x = 1 \cr
& \left. 2 \right)\,\,\,1 + {\tan ^2}x = {\sec ^2}x \cr
& \left. 3 \right)\,\,\,{\cot ^2}x + 1 = {\csc ^2}x \cr} $$
