695 7.2 Verifying Trigonometric Identities Verify that each equation is an identity. See Examples 1–5. 45. cot u csc u = cos u 46. tana sec a = sina 47. 1 - sin2 b cos b = cos b 48. tan2 a + 1 sec a = sec a 49. cos2 u1tan2 u + 12 = 1 50. sin2 b11 + cot2 b2 = 1 51. cot u + tanu = sec u csc u 52. sin2 a + tan2 a + cos2 a = sec2 a 53. cos a sec a + sina csc a = sec2 a - tan2 a 54. sin2 u cos u = sec u - cos u 55. sin4 u - cos4 u = 2 sin2 u - 1 56. sec4 x - sec2 x = tan4 x + tan2 x 57. 1 - cos x 1 + cos x = 1cot x - csc x22 58. 1sec a - tana22 = 1 - sina 1 + sina 59. cos u + 1 tan2 u = cos u sec u - 1 60. 1sec u - tanu22 + 1 sec u csc u - tanu csc u = 2 tanu 61. 1 1 - sinu + 1 1 + sinu = 2 sec2 u 62. 1 sec a - tana = sec a + tana 63. cot a + 1 cot a - 1 = 1 + tana 1 - tana 64. csc u + cot u tanu + sinu = cot u csc u 65. cos u sinu cot u = 1 66. sin2 u11 + cot2 u2 - 1 = 0 67. sec4 u - tan4 u sec2 u + tan2 u = sec2 u - tan2 u 68. sin4 a - cos4 a sin2 a - cos2 a = 1 69. tan2 t - 1 sec2 t = tant - cot t tant + cot t 70. cot2 t - 1 1 + cot2 t = 1 - 2 sin2 t 71. sin2 asec2 a + sin2 acsc2 a = sec2 a 72. tan2 asin2 a = tan2 a + cos2 a - 1 73. tanx 1 + cos x + sinx 1 - cos x = cot x + sec x csc x 74. sinu 1 - cos u - sinu cos u 1 + cos u = csc u11 + cos2 u2 75. 1 + cos x 1 - cos x - 1 - cos x 1 + cos x = 4 cot x csc x 76. 1 + sinu 1 - sinu - 1 - sinu 1 + sinu = 4 tanu sec u 77. 1 - sinu 1 + sinu = sec2 u - 2 sec u tanu + tan2 u 78. sinu + cos u = sinu 1 - cot u + cos u 1 - tanu 79. -1 tana - sec a + -1 tana + sec a = 2 tana 80. 11 + sinx + cos x22 = 211 + sinx211 + cos x2 81. 11 - cos2 a211 + cos2 a2 = 2 sin2 a - sin4 a 82. 1sec a + csc a21cos a - sina2 = cot a - tana 83. 1 - cos x 1 + cos x = csc2 x - 2 csc x cot x + cot2 x
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