Name: ________________________Additional Practice Simplifying/Verifying/Solving TrigonometricIdentities and Equations (Quiz 4 Review)

PART I : Simplify each of the following trigonometric expressions using the fundamental identities.

1. sec(x)cos(x) 2. tan(x)csc(x)

3. sin4x + sin2(x)cos2(x) 4. tan2x – tan2(x)sin2(x)

5. 3sin2x – 5sinx – 2 6. 6cos2x + 5cosx – 6

7. - sin2x + 3cosx + 3 8. tanx – sec2 x

tanx

PART II : Verify each of the following trigonometric identities. Use the fundamental identities to aid you in doing so.

9. sin2x(1 + cot2x) = 1 10. sec(x)∙cos(x) – sin2x = cos2x

11. sin(x)∙csc(x) + cot2x = csc2x 12. cot2x – cos2x = cot2(x)∙cos2(x)

PART III : Solve each of the following trigonometric equations on the interval [0, 2π). Be sure to check for extraneous solutions wherever necessary.

13. 2cosx – 1 = 0 14. 2sinx – 1 = 0

15. tanx = 1 16. 2cosx + √3 = 0

17. tanx + 1 = 0 18. sin2x – 4 = 0

19. 4cos2x – 3 = 0 20. sinx + √2 = - sinx

21. 2sin2x – sinx – 1 = 0 22. tan(x)sin2x = 2tanx