simplifying trig. identities
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“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
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