1. Simplifying Trig. Identities
Chapter5: Analytical Trigonometry
“Simplify identities to sin and cos functions.”

2. Simplifying trig Identity
Example1: simplify tanxcosx
sin x
cos x
tanx cosx
tanxcosx = sin x

3. Simplifying trig Identity
sec x
csc x
Example2: simplify 1
cos x 1
cos x
sinx = x
sec x
csc x 1
sin x =
sin x
cos x
= tan x

4. Simplifying trig Identity
cos2x - sin2x
cos x
Example2: simplify
cos2x - sin2x 1
cos2x - sin2x
cos x
= sec x

5. Practice 1
cos2θ
cosθ
sin2θ cos2θ
secθ-cosθ
csc2θ
cotθ
tan2θ

6. Use pythagorean identity
Example
Simplify:
= cot x (csc2 x - 1)
Factor out cot x
= cot x (cot2 x)
Use pythagorean identity
= cot3 x
Simplify

7. 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

8. Your Turn! Combine fraction Simplify the numerator
Use pythagorean identity
Use Reciprocal Identity