1. What you will learn
How to use the basic trigonometric identities to verify other (more complex) identities
How to find numerical values of trigonometric functions

2. Verifying Trigonometric Identities
We are transforming one side of an equation to look like the other side using trigonometric identities and algebra.
Either side may be transformed into the other side or both sides may be transformed into a simpler “3rd” form.
Objective: 7-2 Verifying Trigonometric Identities

3. Example Verify that sec2x – tan x cot x = tan2x is an identity.
Objective: 7-2 Verifying Trigonometric Identities

4. Steps
1. Transform the more complicated side of the equation to look like the simpler side.
2. Substitute one or more trigonometric identities to simplify expressions.
3. Factor or multiply to simplify expressions.
4. Multiply expression by an expression equal to 1.
5. Express all trigonometric functions in terms of sine and cosine.
Objective: 7-2 Verifying Trigonometric Identities

5. Another Example Verify that is an identity.
Objective: 7-2 Verifying Trigonometric Identities

6. Homework Problem
# #15
Objective: 7-2 Verifying Trigonometric Identities

7. Simplifying Both Sides
Verify that is an identity.
Objective: 7-2 Verifying Trigonometric Identities

8. Another Example Verify that (sec x – tan x)(1 + sin x) = cos x
Objective: 7-2 Verifying Trigonometric Identities

9. More Homework
#19.
Objective: 7-2 Verifying Trigonometric Identities

10. Simplifying Trig Equations - Example
Find a numerical value of one trig function of x if
Objective: 7-2 Verifying Trigonometric Identities

11. You Try Find a numerical value of one trig function of x if
Objective: 7-2 Verifying Trigonometric Identities

12. Homework page 434, 13-16 all, 17, 19, 25, 29, 31 and 33 (challenge)
Objective: 7-2 Verifying Trigonometric Identities