Final answer:
The true statements based on the Pythagorean identities are...
Step-by-step explanation:
The true statements based on the Pythagorean identities are:
1. sine squared (theta) = 1 - cosine squared theta
2. 1 = secant squared theta - tangent squared theta
3. cotangent squared theta = cosecant squared theta - 1
4. 1 - tangent squared theta = negative secant squared theta
5. negative cosine squared theta = sine squared theta - 1
The Pythagorean identities are a set of trigonometric equations that relate the three basic trigonometric functions: sine, cosine, and tangent. These identities are useful in simplifying trigonometric expressions and solving trigonometric equations.