1. Chapter 5 Analytic Trigonometry
Pre-Calculus
OHHS
Mr. J. Focht

2. 5.2 Proving Trig Identities
What You'll Learn
A Proof Strategy
Proving Identities
Disproving Non-Identities
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3. Vocabulary
A Trigonometric Proof is a sequence of expressions showing how to proceed from one given expression and ending at a specified expression.
Each step of the proof will have to be explained.
We usually start with the more complicated expression and work toward the simpler.
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4. Example Show that is an identity. Factor a2-b2=(a-b)(a+b)
Cancel/Reduce
Subtraction
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5. Now You Try
Prove this identity
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6. Rules to Prove By
Do not add, multiply, subtract, divide, use a square root, or square both sides of an identity.
These rules apply only to an equation – we are not dealing with an equation.
Proceed by simple, easily explained steps.
Try to stay on one side of the identity – but there will be exceptions.
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7. Example Prove that LOVE can change to MATH.
Rules: Change only 1 letter each step. Each step must be a word.
LOVE
MOVE
MOTE
MOTH
MATH
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8. Now You Try
Change CAT to DOG
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9. Proving an Identity Prove: tan x + cot x = sec x csc x. Quotient ID
Finding LCD
Fraction Addition
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Continued on the next page

10. Proving an Identity Prove: tan x + cot x = sec x csc x.
Fraction Addition
Def of Fraction Multiplication
Reciprocal ID
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11. Now You Try
Prove: (1-tan x)2 = sec2x – 2 tan x
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12. Example: Using Difference of Squares
Prove:
Multiply by 1
Fraction Multiplication
Cancel/Reduce
Pythagorean ID
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13. Now You Try
Prove:
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14. Example Working on Both Sides
Prove:
Pythagorean ID
Cancel/Reduce
Factor
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Continued on the next page

15. Example Working on Both Sides
Prove:
Factor
Cancel/Reduce
Both sides reduced to the same expression
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16. Now You Try
Prove: sin2x cos3x = (sin2x – sin4x)(cos x)
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17. Disproving Non-Identities
Disproving a non-identity is easy.
Just find 1 value that makes the wannabe identity false.
Example: Prove this to be false.
sin(2x) = 2 sin x
Try x = 30: sin(2∙30) = 2 sin 30
sin 60= 2 sin 30
= 2 (½) is not true
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18. Now You Try
Show that is not an identity.
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19. 5.2 Home Work
P. 460, #2, 7, 12, 16, 20, 24, 28, 34, 36, 46, 50, 58, 59, 62
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