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7.1.2 – Verifying expressions

7.1.2 – Verifying expressions. Recall, we went through several trig identities which may help us convert expressions Using those identities, we can now prove, or disprove, equivalent statements. Guidelines.

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7.1.2 – Verifying expressions

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  1. 7.1.2 – Verifying expressions

  2. Recall, we went through several trig identities which may help us convert expressions • Using those identities, we can now prove, or disprove, equivalent statements

  3. Guidelines • 1) We will usually work with a single side at a time; try to find the “complicated” side, and work with it • 2) Use all trig identities, when possible • 3) Try to get things in terms of sine and cosine, when applicable • Must show “=“ signs in between each step to show the correct flow of information

  4. At the end, both sides should look the same • Will also need some properties from algebra to assist us at times; just keep at it

  5. Example. Verify the following identity: • (1 – cos x)(1 + cos x) = sin2x

  6. Example. Verify the identity • 2csc2x = (1/1-cosx) + (1/1+cosx)

  7. Example. Verify the identity • Sec2(x)/tan(x) = sec(x) csc(x)

  8. Substitutions • In some expressions, it may be beneficial to substitute some kind of trig expression in • Like a combination of algebra and trig

  9. Example. Use the substituion x = tanθ for the expression √(x2 +1).

  10. Example. Use the substitution cos(θ) = x/3 for the expression √(9-x2)

  11. Assignment • Pg. 553 • 16-20 • 27-31 odd

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