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49,55,61

49,55,61

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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49,55,61
\ II. Rewrite in terms of sine and cosine functions: the denominato In Problems 11-20, simplify each trigonometric expression by following the indicated direction. 19. Factor and simplify: sin 0 + 2 sin e + 1 SECTION 7.4 Trigonometric Identities 485 Skill Building he numerator and or by 1 + sing 12. Rewrite in terms of sine and cosine functions: tan e. csc 0. cot 0 sec 0. cos 0 1- sin 0 1 + sin e -by 1 + sin e \ 1L. Multiply sin 6 1 - cos 0 by 1- cos 0" 14. Multiply 15. Rewrite as a single quotient: sin 0 + cos 6 1 + cos 0 cos e - sin 0 16. Rewrite as a single quotient: Cos e sin 0 = cos 6 (sin e + cos 0) (sin e + cos 0) - 1 cos v 1 + cos v 17. Multiply and simplify: (tan 0 + 1) (tan 0 + 1) - sec? 0 sin e cos 0 18. Multiply and simplify: 3 sin e + 4 sin e + 1 tan 0 20. Factor and simplify: cos 0 - 1 cos 0 - cos 0 In Problems 21-100, establish each identity. \21. csc 0- cos 0 = cot 6 22. sec e. sin 0 = tan 0 23. 1 + tan? (-0) = sec? e establish iden 24. 1 + cot? (-0) = csc² 0 25. cos e (tan 0 + cot 0) = csc 0 26. sin 0 (cot 0 + tan 0) = sec 0 27. tan u cot u - cos u = sin? u 28. sin u csc u - cos u = sin? u \ 29. (sec 0 - 1) (sec 0 + 1) = tan? 0 30. (csc 0 - 1) (csc 0 + 1) = cot? 0 31. (sec 0 + tan 6) (sec 0 - tan 0) = 1 32. (csc 0 + cot 0) (csc 0 - cot 0) = 1 33. cos? 0 (1 + tan? 0) = 1 34. (1 - cos 0) (1 + cot? 0) = 1 35. (sin 0 + cos 0)2 + (sin 0 - cos 0)2 = 2 containing the m 36. tan? 0 cos? 0 + cot? 0 sin? e = 1 37. sec* e - sec? 0 = tan 0 + tan? e 38. csc* 0 - csc² 0 = cot 0 + cot? e cotient. cos u sin u 39. sec u - tan u 40. csc u - cot u = 41. 3 sin? 0 + 4 cos? 0 = 3 + cos 0 1 + sin u 1 + cos u nd cosine funcion cos? 0 sin? 0 1 - cos 0 42. 9 sec? 0 - 5 tan? 0 = 5 + 4 sec? 0 43. 1 = sin 0 44. 1 - = - cos 0 1 + sin 0 e of the expresin le. 1 + tan v 45. 1 cot v + 1 1 - sin v csc v - 1 46. csc v +1 sec e 47. csc 0 sin 6 = 2 tan 0 cos 0 tan v cot v - 1 1+ sin v csc e - 1 48. cot 0 1 + sin 0 49. 1 cos 0 + 1 50. cos 0 - 1 cot e csc 0 + 1 1 + seç 0 %3D csc e + 1 sin 6 csc 0 ·1 1 - sec 0 1 - sin v 51. CoS V 1 + sin v sin 0 cos v 1 = 2 sec v 52. = 2 sec v 53. sin 0 - cos 6 %3D cos v 1- sin v sin v cos V 1- cot 0 listed in rad 1 - cos 0 56. 1 + cos 0 sin? 0 sin o 54. 1 = cos 0 = (sec 0 - tan 0)2 (csc 0 – cot 0)2 1 + cos e 1+sin 9 Os 0- sine p cot 0 tan 0 cos 0 57. 1- tan 0 sin 0 sin 0 + cos 58. 1 = 1 + tan 0 + cot 0 cot 0 1 - cot 0 tan 0 1 tan 0 + sec 0 - 1 61. tan 0 - sec 0 + 1 cos e sin 0 cos 0 tan 0 = tan 0 + sec 0 59. tan 0 + 1 + sin 0 = sec 0 60. cos 0 – sin? 0 1- tan? 0 sin 0 sin 0 - cos 0 + 1 62, sin 0 + cos 0 - 1 tan 0 - cot 0 63. tan 0 + cot 0 sec 0 - cos 0 64. sec 0 + cos 0 sin 0 + 1 = sin? 0 – cos² e quations i 1 + cos? 0 cos 0 tan u - cot u 66. tan u + cot u sec 0 + tan 0 67. cot 0 + cos 0 tan u - cot u + 2 cos? u = 1 = tan 0 sec 0 65. tan u + cot u + 1 = 2 sin? u 1 – tan² 0 69. 1 + tan? 6 1 - cot? 0 70. 1 + cot? 0 sind 1 - cos 0 + 2 cos? 0 = 1 seç 0 + 1 = 2 cos? 0 68. 1+ sec 0 sin? 0 sin? 0 – tan 0 72. cos? 0 - cot 0 71 sec 0 – csc 0 tan? 0 73. sec 0 - cos 0 = sin 0 tan 0 71. sec 0 csc 0 = sin 0 - cos 0 1 + sin 0 76. 1 - sin 0 1 - sin 0 1 + sin 0 1 = 2 seç? 0 = 4 tan 0 sec 0 74. tan 0 + cot 0 = sec 0 csc 0 75. sin 0 1 + sin 0 denominatoR
Transcribed Image Text:\ II. Rewrite in terms of sine and cosine functions: the denominato In Problems 11-20, simplify each trigonometric expression by following the indicated direction. 19. Factor and simplify: sin 0 + 2 sin e + 1 SECTION 7.4 Trigonometric Identities 485 Skill Building he numerator and or by 1 + sing 12. Rewrite in terms of sine and cosine functions: tan e. csc 0. cot 0 sec 0. cos 0 1- sin 0 1 + sin e -by 1 + sin e \ 1L. Multiply sin 6 1 - cos 0 by 1- cos 0" 14. Multiply 15. Rewrite as a single quotient: sin 0 + cos 6 1 + cos 0 cos e - sin 0 16. Rewrite as a single quotient: Cos e sin 0 = cos 6 (sin e + cos 0) (sin e + cos 0) - 1 cos v 1 + cos v 17. Multiply and simplify: (tan 0 + 1) (tan 0 + 1) - sec? 0 sin e cos 0 18. Multiply and simplify: 3 sin e + 4 sin e + 1 tan 0 20. Factor and simplify: cos 0 - 1 cos 0 - cos 0 In Problems 21-100, establish each identity. \21. csc 0- cos 0 = cot 6 22. sec e. sin 0 = tan 0 23. 1 + tan? (-0) = sec? e establish iden 24. 1 + cot? (-0) = csc² 0 25. cos e (tan 0 + cot 0) = csc 0 26. sin 0 (cot 0 + tan 0) = sec 0 27. tan u cot u - cos u = sin? u 28. sin u csc u - cos u = sin? u \ 29. (sec 0 - 1) (sec 0 + 1) = tan? 0 30. (csc 0 - 1) (csc 0 + 1) = cot? 0 31. (sec 0 + tan 6) (sec 0 - tan 0) = 1 32. (csc 0 + cot 0) (csc 0 - cot 0) = 1 33. cos? 0 (1 + tan? 0) = 1 34. (1 - cos 0) (1 + cot? 0) = 1 35. (sin 0 + cos 0)2 + (sin 0 - cos 0)2 = 2 containing the m 36. tan? 0 cos? 0 + cot? 0 sin? e = 1 37. sec* e - sec? 0 = tan 0 + tan? e 38. csc* 0 - csc² 0 = cot 0 + cot? e cotient. cos u sin u 39. sec u - tan u 40. csc u - cot u = 41. 3 sin? 0 + 4 cos? 0 = 3 + cos 0 1 + sin u 1 + cos u nd cosine funcion cos? 0 sin? 0 1 - cos 0 42. 9 sec? 0 - 5 tan? 0 = 5 + 4 sec? 0 43. 1 = sin 0 44. 1 - = - cos 0 1 + sin 0 e of the expresin le. 1 + tan v 45. 1 cot v + 1 1 - sin v csc v - 1 46. csc v +1 sec e 47. csc 0 sin 6 = 2 tan 0 cos 0 tan v cot v - 1 1+ sin v csc e - 1 48. cot 0 1 + sin 0 49. 1 cos 0 + 1 50. cos 0 - 1 cot e csc 0 + 1 1 + seç 0 %3D csc e + 1 sin 6 csc 0 ·1 1 - sec 0 1 - sin v 51. CoS V 1 + sin v sin 0 cos v 1 = 2 sec v 52. = 2 sec v 53. sin 0 - cos 6 %3D cos v 1- sin v sin v cos V 1- cot 0 listed in rad 1 - cos 0 56. 1 + cos 0 sin? 0 sin o 54. 1 = cos 0 = (sec 0 - tan 0)2 (csc 0 – cot 0)2 1 + cos e 1+sin 9 Os 0- sine p cot 0 tan 0 cos 0 57. 1- tan 0 sin 0 sin 0 + cos 58. 1 = 1 + tan 0 + cot 0 cot 0 1 - cot 0 tan 0 1 tan 0 + sec 0 - 1 61. tan 0 - sec 0 + 1 cos e sin 0 cos 0 tan 0 = tan 0 + sec 0 59. tan 0 + 1 + sin 0 = sec 0 60. cos 0 – sin? 0 1- tan? 0 sin 0 sin 0 - cos 0 + 1 62, sin 0 + cos 0 - 1 tan 0 - cot 0 63. tan 0 + cot 0 sec 0 - cos 0 64. sec 0 + cos 0 sin 0 + 1 = sin? 0 – cos² e quations i 1 + cos? 0 cos 0 tan u - cot u 66. tan u + cot u sec 0 + tan 0 67. cot 0 + cos 0 tan u - cot u + 2 cos? u = 1 = tan 0 sec 0 65. tan u + cot u + 1 = 2 sin? u 1 – tan² 0 69. 1 + tan? 6 1 - cot? 0 70. 1 + cot? 0 sind 1 - cos 0 + 2 cos? 0 = 1 seç 0 + 1 = 2 cos? 0 68. 1+ sec 0 sin? 0 sin? 0 – tan 0 72. cos? 0 - cot 0 71 sec 0 – csc 0 tan? 0 73. sec 0 - cos 0 = sin 0 tan 0 71. sec 0 csc 0 = sin 0 - cos 0 1 + sin 0 76. 1 - sin 0 1 - sin 0 1 + sin 0 1 = 2 seç? 0 = 4 tan 0 sec 0 74. tan 0 + cot 0 = sec 0 csc 0 75. sin 0 1 + sin 0 denominatoR
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