SECTION 7.4 Trigonometric Identities Skill Building In Problems 11-20, simplify each trigonometric expression by following the indicated direction. \I1. Rewrite in terms of sine and cosine functions: he numerator and \ 13. Multiply 15. Rewrite as a single quotient: MIS + ha 40 12. Rewrite in terms of sine and cosine functions: tan 0. csc 6. cot 0 sec 0. 1 + sin 0 by 1 + sin 0 cos 0 sin 0 14. Multiply sin 0 cos 0 1+ cos 0 by 1. cos e 16. Rewrite as a single quotient: sin 0 + cos 0 cos e - sin 0 1. 1- cos v sin 0 %3D cos 0 1. cos 6 (sin e + cos 0) (sin 0+ cos 0) 1 + cos v 1. 17. Multiply and simplify: (tan 0 + 1) (tan 0 + 1) - se sin e cos 0 3 sin? 0 + 4 sin e + 1 sin e + 2 sin 0 + 1 18. Multiply and simplify: tan 0 19. Factor and simplify: cos 0 - 1 20. Factor and simplify: cos e cos e In Problems 21-100, establish each identity. = cot 0 22. sec 0- sin 0 = tan 0 21. csc 0· cos e 23. 1 + tan (-0) sec? e establish ideni 24. 1+ cot (-0) = csc? e 25. cos 0 ( tan 6 + 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) = tan² e %3D 30. (csc 0 – 1) (csc 0 + 1) = cot? 0 31. (sec 0 + tan 0) (sec 0 - tan 0) = 1 32. (csc 0 + cot 0) (csc 0 - cot 0) 33. cos 0 (1 + tan? 0) = 1 34. (1 - cos 6) (1 + cot? e) = 1 35. (sin 0 + cos 0)2 + (sin 0 - cos containing the m 36. tan 0 cos? 0 + cot? 0 sin? e = 1 37. sec* e - sec² 0 = tan 0 + tan? e 38. csc* 0 - csc2 0 = cot e + cot? cotient. Cos u sin u 39. sec u - tan u = 1 + sin u 40. csc u - cot u = 41. 3 sin e + 4 cos 0 = 3 + cos? E 1 + cos u nd cosine funci cos? 0 sin? 0 1 - cos 0 42. 9 sec? 0 - 5 tan? 0 = 5 + 4 sec e 43. 1 = sin 0 - cos 0 44. 1 - 1 + sin 0 e of the expresin le. 1 - sin v 1 + sin v 1 + tan v 45. cot v + 1 csc v - 1 46. sin sec 0 47. csc e 2 tan 0 tan v cot v - csc v + 1 cos 0 csc e - 1 48. cot 0 1 + sin 0 49. csc 0 + 1 cos 0 + 1 50. cos 0 cot e 1 + sec 0 csc 0 + 1 sin 6 csc 0 - 1 1 sec 0 1 - sin v cos v COS V 1 + sin v sin 0 1 \51. 52. = 2 sec v 53. sin 0 - cos 0 2 sec v cos v 1 - sin v 1 sin v Cs v 1 - cot 0 listed in red sin 0 : - sin 0 = (sec 0- tan 0)2 1- cos 0 56. 1 + cos 0 54. 1 - = cos 0 (csc 0 - cot 0) 1 + cos 0 1 + sin 9 cos 0 sin 0 cot 0 tan 0 57. 1 - tan 0 sin 0+ cos 58. 1 - tan 0 = 1 + tan 0 + cot 0 %3D 1 - cot 0 1 - cot 0 Ços e sin 0 cos 0 tan 0 tan 0 + sec 0 - 1 61 ton 0 denomincal the denominator
SECTION 7.4 Trigonometric Identities Skill Building In Problems 11-20, simplify each trigonometric expression by following the indicated direction. \I1. Rewrite in terms of sine and cosine functions: he numerator and \ 13. Multiply 15. Rewrite as a single quotient: MIS + ha 40 12. Rewrite in terms of sine and cosine functions: tan 0. csc 6. cot 0 sec 0. 1 + sin 0 by 1 + sin 0 cos 0 sin 0 14. Multiply sin 0 cos 0 1+ cos 0 by 1. cos e 16. Rewrite as a single quotient: sin 0 + cos 0 cos e - sin 0 1. 1- cos v sin 0 %3D cos 0 1. cos 6 (sin e + cos 0) (sin 0+ cos 0) 1 + cos v 1. 17. Multiply and simplify: (tan 0 + 1) (tan 0 + 1) - se sin e cos 0 3 sin? 0 + 4 sin e + 1 sin e + 2 sin 0 + 1 18. Multiply and simplify: tan 0 19. Factor and simplify: cos 0 - 1 20. Factor and simplify: cos e cos e In Problems 21-100, establish each identity. = cot 0 22. sec 0- sin 0 = tan 0 21. csc 0· cos e 23. 1 + tan (-0) sec? e establish ideni 24. 1+ cot (-0) = csc? e 25. cos 0 ( tan 6 + 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) = tan² e %3D 30. (csc 0 – 1) (csc 0 + 1) = cot? 0 31. (sec 0 + tan 0) (sec 0 - tan 0) = 1 32. (csc 0 + cot 0) (csc 0 - cot 0) 33. cos 0 (1 + tan? 0) = 1 34. (1 - cos 6) (1 + cot? e) = 1 35. (sin 0 + cos 0)2 + (sin 0 - cos containing the m 36. tan 0 cos? 0 + cot? 0 sin? e = 1 37. sec* e - sec² 0 = tan 0 + tan? e 38. csc* 0 - csc2 0 = cot e + cot? cotient. Cos u sin u 39. sec u - tan u = 1 + sin u 40. csc u - cot u = 41. 3 sin e + 4 cos 0 = 3 + cos? E 1 + cos u nd cosine funci cos? 0 sin? 0 1 - cos 0 42. 9 sec? 0 - 5 tan? 0 = 5 + 4 sec e 43. 1 = sin 0 - cos 0 44. 1 - 1 + sin 0 e of the expresin le. 1 - sin v 1 + sin v 1 + tan v 45. cot v + 1 csc v - 1 46. sin sec 0 47. csc e 2 tan 0 tan v cot v - csc v + 1 cos 0 csc e - 1 48. cot 0 1 + sin 0 49. csc 0 + 1 cos 0 + 1 50. cos 0 cot e 1 + sec 0 csc 0 + 1 sin 6 csc 0 - 1 1 sec 0 1 - sin v cos v COS V 1 + sin v sin 0 1 \51. 52. = 2 sec v 53. sin 0 - cos 0 2 sec v cos v 1 - sin v 1 sin v Cs v 1 - cot 0 listed in red sin 0 : - sin 0 = (sec 0- tan 0)2 1- cos 0 56. 1 + cos 0 54. 1 - = cos 0 (csc 0 - cot 0) 1 + cos 0 1 + sin 9 cos 0 sin 0 cot 0 tan 0 57. 1 - tan 0 sin 0+ cos 58. 1 - tan 0 = 1 + tan 0 + cot 0 %3D 1 - cot 0 1 - cot 0 Ços e sin 0 cos 0 tan 0 tan 0 + sec 0 - 1 61 ton 0 denomincal the denominator
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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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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