1. Fundamental
Trigonometric Identities
Essential Questions
How do we use fundamental trigonometric identities to simplify and rewrite expressions and to verify other identities?
Holt McDougal Algebra 2
Holt Algebra 2

2. You can use trigonometric identities to simplify trigonometric expressions. Recall that an identity is a mathematical statement that is true for all values of the variables for which the statement is defined.

3. To prove that an equation is an identity, alter one side of the equation until it is the same as the other side. Justify your steps by using the fundamental identities.

4. Proving Trigonometric Identities
Prove each trigonometric identity. 1.
Choose the right-hand side to modify.
Reciprocal identities.
Simplify.
Ratio identity.

5. Proving Trigonometric Identities
Prove each trigonometric identity.
1 – cot θ = 1 + cot(–θ) 2.
Choose the right-hand side to modify.
Reciprocal identity.
Negative-angle identity.
= 1 + (–cotθ)
Reciprocal identity.
= 1 – cotθ
Simplify.

6. You may start with either side of the given equation
You may start with either side of the given equation. It is often easier to begin with the more complicated side and simplify it to match the simpler side.
Helpful Hint

7. Proving Trigonometric Identities
Prove each trigonometric identity.
sin θ cot θ = cos θ 3.
Choose the left-hand side to modify.
Ratio identity.
cos θ =
Simplify.

8. Proving Trigonometric Identities
Prove each trigonometric identity.
Choose the left-hand side to modify.
1 – sec(–θ) = 1 – secθ 4.
Reciprocal identity.
Negative-angle identity.
Reciprocal Identity.

9. Proving Trigonometric Identities
Prove each trigonometric identity.
Reciprocal identity.

10. Proving Trigonometric Identities
Prove each trigonometric identity.
Reciprocal identity.

11. Proving Trigonometric Identities
Prove each trigonometric identity.
Tan and Cot identity.
Common Denominator
Reciprocal identity.

12. Proving Trigonometric Identities
Prove each trigonometric identity.
Factor out a sin x
Distributive property

13. Lesson 11.3 Practice A