The lengths of the sides of the right triangle shown in the figure are 3, 4, and 5. Find the areas of the squares on the three sides, and find a relationship between them.
Consider the identity . We can use this to derive two new identities.
First, divide both sides of the identity by to find an identity in terms of and .
Now, divide both sides of the identity through by to find an identity in terms of and .
The figure shows a unit circle and a radius with the lengths of its - and -components. Use the Pythagorean theorem to derive an identity connecting the lengths 1, , and .