1. 3.9 Proving Trig Identities

2. Using fundamental identities (from 3-8), we can prove other identities
Best way is to start with one side and manipulate algebraically or use fundamental identities to get it to be equivalent to other side
Note: There are no “hard fast” rules to adhere to… sometimes we just have to try something.
Hints: – try writing in its component parts or reciprocal
– add fractions (common denominator)
– multiply fraction by conjugate of bottom
– utilize Pythagorean identities
If it asks for a “counterexample” you need to find just one value that it will not work for.
(it might actually work for some values – so think about your choice)
(all sines
& cosines)

3. Let’s try some!!!
There are 6 problems around the classroom.
Work your way around the room doing as many problems as you can
Use your friends for help

4. Ex 1) Prove:
Work more complicated side

5. Ex 2) Prove: Work this side Write in terms of sinϕ & cosϕ
Pythag Ident 
(cos2θ + sin2θ = 1)

6. Ex 3) Prove: Work this side Mult by conj of bottom
Pythag identity (cos2θ + sin2θ = 1) 1
secθ & cosθ are reciprocals!

7. Ex 4) Prove: Work this side Write tanθ in terms of sinθ & cosθ
cscθ & sinθ are reciprocals!
Use Pythag identity (cos2θ + sin2θ = 1)
cosθ & secθ 
are reciprocals!

8. Ex 5) Show that sin(β + θ) = sinβ + sinθ is not an identity.
You just need 1 counterexample.
There are lots of answers!!
Here is just one:
LHS:
RHS:

9. Ex 6) Prove: Work this side Diff of 2 squares 1
Pythag identity (cos2θ + sin2θ = 1)