1. One way to use identities is to simplify expressions involving trigonometric functions. Often a good strategy for doing this is to write all trig functions in terms of sines and cosines and then simplify.
substitute using each identity
simplify

2. Simplify: 1. 𝑐𝑠𝑐𝜃 𝑐𝑜𝑡𝜃 2. 𝑐𝑜𝑠𝑥𝑐𝑠𝑐𝑥𝑡𝑎𝑛𝑥 3. 𝑐𝑜𝑠𝑥𝑐𝑜𝑡𝑥+𝑠𝑖𝑛𝑥
1. 𝑐𝑠𝑐𝜃 𝑐𝑜𝑡𝜃 𝑐𝑜𝑠𝑥𝑐𝑠𝑐𝑥𝑡𝑎𝑛𝑥 3. 𝑐𝑜𝑠𝑥𝑐𝑜𝑡𝑥+𝑠𝑖𝑛𝑥
4. 𝑠𝑒𝑐𝑥 𝑐𝑠𝑐𝑥 𝑐𝑜𝑠 2 𝑥+ 𝑠𝑖𝑛 2 𝑥 cos 𝑥 𝑐𝑠𝑐 2 𝑥𝑐𝑜𝑡𝑥−𝑐𝑜𝑡𝑥
7. 𝑡𝑎𝑛𝑥𝑠𝑖𝑛𝑥+𝑐𝑜𝑠𝑥 𝑠𝑒𝑐𝑡 𝑡𝑎𝑛𝑡 − 𝑡𝑎𝑛𝑡 1+𝑠𝑒𝑐𝑡
9. (1 + tan x)2 - 2 sin x sec x 𝑐𝑠𝑐𝑥 𝑡𝑎𝑛𝑥+𝑐𝑜𝑡𝑥

3. Simplifying Trig expressions3. 1. 2.
Reciprocal Identity
Quotient Identity
Quotient Identity
Change to LCD
Reciprocal Identity
Quotient Identity
Reciprocal Identity
Pythagorean Identity
Reciprocal Identity

4. Simplifying trig Expressions
sec x
csc x 4. 1
cos x 1
cos x
sinx = x
Reciprocal Identities
sec x
csc x 1
sin x =
sin x
cos x
Quotient Identity
= tan x

5. Simplifying trig Expressions5.
cos2x + sin2x
cos x
cos2x - sin2x 1
= sec x
cos2x - sin2x
cos x
Pythagorean Identity
Reciprocal Identity

6. Simplifying trig Expressions6.
= cot x (csc2 x - 1)
Factor out cot x
= cot x (cot2 x)
Pythagorean Identity
= cot3 x
Simplify

7. Simplifying trig Expressions7.
= sin x (sin x) + cos x
cos x
Quotient Identity
cos2x
cos x
Change fraction with LCD
= sin2 x + (cos x)
cos x
= sin2 x + cos2x
cos x
Add =
cos x
Pythagorean Identity
= sec x
Reciprocal Identity

8. Simplifying trig Expressions8.
Combine fraction
Simplify the Numerator
Pythagorean Identity
Simplify
Reciprocal Identity

9. 10. 9. Simplifing Trigonometric Expressions
c) (1 + tan x)2 - 2 sin x sec x d)