1. 12. MORE on TRIG IDENTITIES

2. Example Simplify: = sin x (sin x) + cos x Use quotient identity cos x
Simplify fraction with LCD
= sin2 x + (cos x)
cos x
= sin2 x + cos2x
cos x
Simplify numerator =
cos x
Use pythagorean identity
= sec x
Use reciprocal identity

3. Examples!
Rewrite

4. Rewrite

5. Rewrite

6. Rewrite

7. Rewrite

8. Rewrite

9. Verify the following identity:
Let's sub in here using reciprocal identity

10. Establish the following identity:
Let's sub in here using reciprocal identity and quotient identity
combine fractions
Another trick is if you have two terms with one term a 1 and the other a sine or cosine, multiply top and bottom of the fraction by the conjugate and then you'll be able to use the Pythagorean Identity

11. Hints for Establishing Identities
Work on the more complex side first
If there are 2 fractions added or subtracted, get a common denominator
If there is 1 fraction with 2 terms on top and 1 on bottom, split into 2
If you have squared functions paired with a 1, look for Pythagorean Identities
If you can distribute, you should
If you can factor, you should
If you have a fraction with (1 + trig function) try multiplying top & bottom by conjugate and use Pythagorean Identity
Write everything in terms of sines and cosines using reciprocal and quotient identities
Have fun with these---it's like a puzzle, can you use identities and algebra to get them to match!