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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 59E
icon
Related questions
Topic Video
Question
13,19,25
\ 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
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,