Pre calculus Problems of the Day Simplify the following:

Trigonometric Identities - a statement of equality that is true for all values where the function is defined. Reciprocal Identities: Quotient Identities:

Pythagorean Identities:Even/Odd Identities:

Verifying Trigonometric Identities To verify a trigonometric identity we must show that one side of the identity can be simplified so that it is identical to the other side or each side can be simplified independently until they are identical. Never treat an identity like an equation. We are not solving for the variable.

WE VERIFY (OR PROVE) IDENTITIES BY DOING THE FOLLOWING: Work with one side at a time. We want both sides to be exactly the same. Start with the more complicated side Use algebraic manipulations and/or the basic trigonometric identities until you have the same expression as on the other side.

Techniques for verifying trigonometric identities. 1)Rename using the fundamental identities. 2)Rewrite a more complicated side in terms of sines and cosines. 3)Factor. 4)Combine fractional expressions using an LCD. 5)Separate a single-term quotient into two terms. 6)Multiply the numerator and denominator on one side by a binomial factor that appears on the other side of the identity.

Verifying Trigonometric Identities