1. 5.2 Proving Trigonometric Identities
Dust off those thinking caps…it’s time to do some proofs!

2. 5.2 Proving Trigonometric Identities
In this lesson you’ll learn about:
Strategies for proving
Proving identities
Disproving non-identities
Identities in Calculus

3. Do Now (With a partner) Discuss ways you would prove:
x3 – x2 _ (x-1)(x+1) = 1 – x x

4. General Strategies for Proofs
The proof begins with the expression on one side and ends with the expression on the other side.
The proof in between shows a series of equivalent expressions that is easy to follow.
The algebra is the proof; you don’t have to write anything but the steps.

5. Strategies for Proofs cont.
Simplify the MORE COMPLEX side to be identical to the less complex side.
You can go LHS RHS or RHS LHS
If all else fails, re-express every trig. function in terms of sine and cosine and use trig. identities to simplify.

6. Even More Strategies for Proofs
Combine fractions by using common denominators.
Use the Pythagorean Identities for differences of squares.
Always be mindful of the expression you need to work towards. Begin with the end in mind, and do manipulations that will help you reach that goal, even if that means you simplify both sides and meet in the middle.

7. Ex 1 Prove the identity:
(1 – tan x)2 = sec2x – 2 tan x

8. Ex 2 Prove 1 + 1 = 2sec2x 1 + sin x 1 – sin x

9. Ex 3 Prove the identity:

10. Ex 4 Prove the identity:

11. Exit Ticket (With a partner and turn in before you leave class today)
P Ex #11, 29, 31, 44
Show your work for full credit
Turn in 1 paper for both of you
Please include both of your names on your paper!!
Talking limited to discussion of these problems only!!