One way to use identities is to simplify

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

SIMPLIFY:

SIMPLIFYING TRIG EXPRESSIONS 1. 3. 2. Quotient Identity Reciprocal Identity Quotient Identity Change to LCD Reciprocal Identity Quotient Identity Reciprocal Identity Pythagorean Identity Reciprocal Identity

SIMPLIFYING TRIG EXPRESSIONS sec x 4. csc x Reciprocal Identities Quotient Identity 1 cos sec xx csc 1 x sin x = 1 sinx x cos x 1 = sin x cos x = tan x

SIMPLIFYING TRIG EXPRESSIONS 5. cos 2 x + sin 2 x cos 2 x - sin 12 x cos x = sec x Pythagorean Identity Reciprocal Identity

SIMPLIFYING TRIG EXPRESSIONS 6. = cot x (csc 2 x - 1) Factor out cot x = cot x (cot 2 x) Pythagorean Identity = cot 3 x Simplify

SIMPLIFYING TRIG EXPRESSIONS 7. = sin x (sin x) + cos x 2 x cos 2 = sin x + (cos x) cos x = sin 2 x + cos 2 x cos x = 1 cos x = sec x Quotient Identity Change fraction with LCD Add Pythagorean Identity Reciprocal Identity

SIMPLIFYING TRIG EXPRESSIONS 8. Combine fraction Simplify the Numerator Pythagorean Identity Simplify Reciprocal Identity

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