“Simplify identities to sin and cos

functions.”

Simplifying Trig. Identities

Chapter5: Analytical Trigonometry

Simplifying trig Identity

Example1: simplify tanxcosx

tanx cosxsin xcos x

tanxcosx = sin x

Example2: simplifysec xcsc x

sec xcsc x1sin x

1cos x 1

cos xsinx

1= x

=sin xcos x

= tan x

Simplifying trig Identity

Simplifying trig Identity

Example2: simplify cos2x - sin2x

cos x

cos2x - sin2x

cos xcos2x - sin2x 1 = sec x

Practice

1 cos2θ cosθ sin2θ cos2θ

secθ-cosθ csc2θ cotθ tan2θ

ExampleSimplify:

= cot x (csc2 x - 1)

= cot x (cot2 x)

= cot3 x

Factor out cot x

Use pythagorean identity

Simplify

ExampleSimplify:

Use quotient identity

Simplify fraction with LCD

Simplify numerator

= sin x (sin x) + cos xcos x

= sin2 x + (cos x)cos x

cos xcos x

= sin2 x + cos2x

cos x = 1

cos x

= sec x

Use pythagorean identity

Use reciprocal identity

Your Turn!Combine fraction

Simplify the numerator

Use pythagorean

identityUse

Reciprocal Identity