687 7.1 Fundamental Identities Concept Check For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten. I 39. -tanx cos x = _____ 40. sec2 x - 1 = _____ 41. sec x csc x = _____ 42. 1 + sin2 x = _____ 43. cos2 x = _____ II A. sin2 x cos2 x B. 1 sec2 x C. sin1-x2 D. csc2 x - cot2 x + sin2 x E. tan x 44. A student writes “1 + cot2 = csc2.” Comment on this student’s work. 45. Concept Check Suppose that cos u = x x + 1 . Find an expression in x for sinu. 46. Concept Check Suppose that sec u = x + 4 x . Find an expression in x for tanu. Perform each transformation. See Example 2. 47. Write sin x in terms of cos x. 48. Write cot x in terms of sin x. 49. Write tan x in terms of sec x. 50. Write cot x in terms of csc x. 51. Write csc x in terms of cos x. 52. Write sec x in terms of sin x. Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of u only. See Example 3. 53. cot u sinu 54. tanu cos u 55. sec u cot u sinu 56. csc u cos u tanu 57. cos u csc u 58. sinu sec u 59. sin2 u1csc2 u - 12 60. cot2 u11 + tan2 u2 61. 11 - cos u211 + sec u2 62. 1sec u - 121sec u + 12 63. 1 + tan1-u2 tan1-u2 64. 1 + cot u cot u 65. 1 - cos21-u2 1 + tan21-u2 66. 1 - sin21-u2 1 + cot21-u2 67. sec u - cos u 68. csc u - sinu 69. 1sec u + csc u21cos u - sinu2 70. 1sinu - cos u21csc u + sec u2 71. sinu1csc u - sinu2 72. cos u1cos u - sec u2 73. 1 + tan2 u 1 + cot2 u 74. sec2 u - 1 csc2 u - 1 75. csc u cot1-u2 76. tan1-u2 sec u 77. sin21-u2 + tan21-u2 + cos21-u2 78. -sec21-u2 + sin21-u2 + cos21-u2
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