7.1 Trig Identities Simplifying Trig Expressions Proving Trig Identities

Fundamental Trig Identities Reciprocal Identities: Tangent/Cotangent Identities: Pythagorean Identities:

Example 1 Simplify the trig expression: Solution:

Example 2 Simplify the expression: Answer:

Example 3 Simplify the expression: Solution:

Tips for Proving Trig Identities Start with one side of the equation and manipulate it until it equals the other side. (Try the more complicated side first!) Look for chances to use identities and/or algebraic techniques (adding fractions, factoring, multiplying by a form of “1”, etc.) If you get stuck, try re-writing everything in terms of the sine and cosine. * Can also try working with each side of the equation separately until you obtain the same expression.

Example 4 Prove the identity:

Example 5 Verify the identity: