In Try This 4 you may have found that sin θ and cos θ are related by the identity sin2 θ + cos2 θ = 1 by drawing a diagram similar to the diagram shown. You also saw that 1 + tan2 θ = sec2 θ and 1 + cot2 θ = csc2 θ. As such, they are identities. These are called Pythagorean identities because each can be derived from the Pythagorean theorem, a2 + b2 = c2.
Watch “Pythagorean Identity Derivation” to see another derivation of these identities.
Read “Example 3” on page 295 of the textbook. Pay attention to how the identity is verified numerically.