7.1.2 – Verifying expressions

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