1. Pre-calc w-up 2/16 2. Simplify cos2 x tan2 x + cos2x
Using trig identities
2. Simplify cos2 x tan2 x + cos2x
Answers: / cos50o

2. 7.2 Verifying Trig Identities
Verifying trig identities algebraically involves transforming one side of the equation into the same form as the other side using basic trig identities and properties of algebra.

3. Suggestions for verifying :
Start with the more complicated side: you are trying to get it to match the simpler side.
Get a common denominator
Substitute one or more basic trig functions.
Ex: you see 1, replace it with sin2x + cos2x
Factor or multiply to simplify expressions
Ex: sin2x – cos2x = (sinx – cosx)(sinx + cosx)
Multiply expression by an expression of 1
Remember the fancy form of 1, same #/same#
Express all trig function in terms of sine and cosine
Ex: you see secx replace it with 1/cosx

4. Review of Pythagorean identities
Can also be written: cos2q = 1 – sin2q
(subtracted sin2 from both sides)
or : sin2q = 1 – cos2q
What about these:: sin2q – 1 = – cos2q
cos2q – 1 = – sin2q
tan2 q = sec2q – 1
sec2 q – tan2 q = 1
cot2 q = csc2q – 1
csc2 q – cot2 q = 1

5. Ex1: Verify the identity sec2x – tanxcotx = tan2x
left
Which side should we start with?
Re-write everything using sin & cosine
Simplify
Substitute sec2x with a basic trig function
Yeah the right side matches the left 
sec2x – 1 =
tan2x + 1 – 1 =
tan2x = tan2x

6. Ex2: You try: Hint: you should recognize this is an identity 
Substituted a basic a trig identity
Simplified
Wrote it as sine and cosine
simplified

7. Ex3: find a numerical value of one trig function of x if
You can work with both sides of the equation in these type of problems
Start by rewriting using sine/cosine
Simplify
Keep simplifying
Goal – to write it as ONE trig function

8. Ex4: little more difficult, but you can do it: find a numerical value of one trig function of x if
How to start oh how to start? I know lets get a common denominator

9. Summary: Homework: Tues/Wed pg 434 # 13-28
Thur pg 434 # and ws
You must show your work