724 CHAPTER 7 Trigonometric Identities and Equations These summary exercises provide practice with the various types of trigonometric identities presented in this chapter. Verify that each equation is an identity. 1. tan u + cot u = sec u csc u 2. csc u cos2 u + sin u = csc u 3. tan x 2 = csc x - cot x 4. sec1p - x2 = - sec x 5. sin t 1 + cos t = 1 - cos t sin t 6. 1 - sin t cos t = 1 sec t + tan t 7. sin 2u = 2 tan u 1 + tan2 u 8. 2 1 + cos x - tan2 x 2 = 1 9. cot u - tan u = 2 cos2 u - 1 sin u cos u 10. 1 sec t - 1 + 1 sec t + 1 = 2 cot t csc t 11. sin1x + y2 cos1x - y2 = cot x + cot y 1 + cot x cot y 12. 1 - tan2 u 2 = 2 cos u 1 + cos u 13. sin u + tan u 1 + cos u = tan u 14. csc4 x - cot4 x = 1 + cos2 x 1 - cos2 x 15. cos x = 1 - tan2 x 2 1 + tan2 x 2 16. cos 2x = 2 - sec2 x sec2 x 17. tan2 t + 1 tan t csc2 t = tan t 18. sin s 1 + cos s + 1 + cos s sin s = 2 csc s 19. tan 4u = 2 tan 2u 2 - sec2 2u 20. tan a x 2 + p 4b = sec x + tan x 21. cot s - tan s cos s + sin s = cos s - sin s sin s cos s 22. tan u - cot u tan u + cot u = 1 - 2 cos2 u 23. tan1x + y2 - tan y 1 + tan1x + y2 tan y = tan x 24. 2 cos2 x 2 tan x = tan x + sin x 25. cos4 x - sin4 x cos2 x = 1 - tan2 x 26. csc t + 1 csc t - 1 = 1sec t + tan t22 Summary Exercises on Verifying Trigonometric Identities 7.5 Inverse Circular Functions ■ Review of Inverse Functions ■ Inverse Sine Function ■ Inverse Cosine Function ■ InverseTangent Function ■ Other Inverse Circular Functions ■ Inverse Function Values Review of Inverse Functions Recall that if a function is defined so that each range element is used only once, then it is a one-to-one function. For example, the function ƒ1x2 = x3 is a one@to@one function because every real number has exactly one real cube root. However, g1x2 = x2 is not a one@to@one function because g122 = 4 and g1-22 = 4. There are two domain elements, 2 and -2, that correspond to the range element 4.
RkJQdWJsaXNoZXIy NjM5ODQ=