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8.1 please do no 40, 74 from the picture In Problems 9-36, find the exact value of each expression. 9. cos sin - 10. sin
8.1 please do no 40, 74 from the picture
In Problems 9-36, find the exact value of each expression. 9. cos sin - 10. sin cos 11. tan cos 1( - V3 12. tan sin (- )] 13. sec cos 1 1 14. cot sin '(- !) 15. csc (tan $ 1) 16. sec ( tan 1 V3) 17. sin [ tan ' (-1) ] 18. cos sin (- 3) 19. sec sin (- 2) ] 20. CSC Cos (- 3) 21. cos-1( sin ST) 22. tan cot 27 3 23. sin cos (- a) 24. cos i tan ( - # ) ] 25. tan sin 1 1) 26. tan cos 1 27. sec( tan 1 1 ) 28. cos sin 1 V2\ 3 29. cot sin (-12) 30. csc [ tan (-2) ] 31. sin [ tan (-3) ] 32. cot cost1( - 3 )] 33. sec sin 1 2VS 34. csc tan-1 1) 35. sin 1 cos 3TT 7 TT 4 36. cos 1 sin 6 In Problems 37-44, find the exact value of each expression. 37. cot-1 V3 38. cot 1 1 39. csc (-1) 40. csc-1 V2 41. sec-1 2 V3 42. sec (-2) 43. cot-1(_ V3) 44. csc-1/ _ 2V/3 3 3 3In Problems 21-100, establish each identity. 21. esc d . cos # = cot # 22. sec # - sin d = tan # 23. 1 + tan' (-0) = sec- d 24. 1 + cot (-8) = csco 25. cos # ( tan # + cot #) = csco 26. sin # ( cot # + tan #) = sec # 27. tan u cot u - cos u = sin u 28. sin u csew - cos u = sin u 29. (seco - 1) (seco + 1) = tan d 30. (cse # - 1) (csco + 1) = cote 31. (seco + tan d) (seco - tan d) = 1 32. (csco + cot #) (csco - cot #) = 1 33. cos e (1 + tan #) = 1 34. (1 - cos' #) (1 + cot #) = 1 35. (sin # + cos #)2 + (sin # - cos #) ? = 2 36. tan 0 cos 0 + cot' 0 sin' 0 = 1 37. secto - sec' 0 = tan' 0 + tano 38. cact 0 - cac' 0 = cot* 0 + cot3 0 39. secu - tan u = = COS HI sin u 1 + sin u 40. escu - cot u = 1 + cos u 41. 3 sin 9 + 4 cos- 0 = 3 + cos3 0 42. 9 sec-8 - 5 tan' 8 = 5 + 4 sec- A 43. 1 - cos- 8 = sin # 44. 1 - sin- 8 1 + sin d - DOS H coS O 45. 1 + tan v cot v + 1 46. CSC V - 1 1 - sin v 47. Sec 6 sin 8 - tan v cot v - ese v + 1 1 + sin CSC A = 2 tan BOS A 48. CSC 8 - cot a 19. 1 + sin e cac e + 1 cos # + 1 1 + sec 6 cot # csc # + 1 1 - sin # CSC # - 1 50. COS # - 1 1 - sec # 51. - sin v COS V = 2 sec v COS V COS V sin v 52. 1 + sin v - = 2 sec v sin # 1 + sin v 53. COS V sind - cos d - cote sinto 54. 1 COS B - sin d 55. 1 + sing (sec # - tan o) ? - cos 8 1 + cos & 56. 1 + cos 8 (csef - coto) 2 COS 0 57. sin o 1 - tan o 1 - cot d = sin d + cos o cot 9 58. tan e + 1 - tan d 1 - cot # = 1 + tand + coto 59. tan # + - COS d sece 1 + sin 0 60. sin d cos tan o 61. tan d + seco - 1 cos 8 - sin a 1 - tan e tan d - seco + 1 = tan 8 + sec e 62. sin 0 - cos 0 + 1 sin d + 1 63. tan 8 - cot sec d - cos d sin # + cos 8 - tan # + cot a sin' 8 - cos- 0 64. sino COS B sece + cos a 1 + cos' d 65. tan i - cot # + 1 = 2sin a tan # - cot u tan u + opt a -+ 2 cos 1 = 1 67. seco + tan e tan a + cot u = tan 8 sec e cote + cos 8 sec 8 68. 1 - cos e 69 1 - tan- e + 1 = 2 cos- # 1 - col- 8 sing 1 + tan- 0 70. 1 + cot- 0 - + 2 cos # = 1 71 Sec a - csc # = sin 8 - case 72. sin- 8 - tan 8 Sec A CSC 8 = tane cos # - cote 73. sec # - cos # = sin A tan A 74. tan a + cote = seco esce 75. 1 + sine 1 - sind 1 - sind 1 + sin = 2 soc3 8 76. 1 - sin d 1 + sin d = 4 tan 0 sec eIn Problems 39-58, find the exact value, if any, of each composite function. If there is no value, say it is "not defined." Do not use a calculator. 39. cos 1 cos 47 5 40. sin -1 sin (- 10 41. tan 1 tan( - 3+ 42. sin-1 sin(- 3 ) 43. sin 1(sin 97 44. cos 1 cos(- ) 45. tan -1tan 46. tantan(- 2+ 47 . cos [ cos ( - # ) 48 . sin [ sin ( - 34 ) 49. tan-1 tan( ) 50. tan tan(- 3w 51. sin( sin 1 ) 52. cos Cos (- ) 53. tan ( tan '4) 54. tan tan '(-2) ] 55. cos ( cos '1.2) 56. sin [ sin-1 (-2) ] 57. tan ( tan 'T) 58. sin [ sin ' (-1.5) ] In Problems 59-66, find the inverse function f-of each function f. Find the range of f and the domain and range of f. 59. f(x) = 5 sin x + 2; - 60. f(x) = 2 tan x - 3; - "Step by Step Solution
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