708 CHAPTER 7 Trigonometric Identities and Equations Write each function as an expression involving functions of u or x alone. See Example 4. 63. cos1u - 180°2 64. cos1u - 270°2 65. cos1180° + u2 66. cos1270° + u2 67. cos160° + u2 68. cos145° - u2 69. cos a 3p 4 - xb 70. sin145° + u2 71. tan1u + 30°2 72. tana p 4 + xb 73. sina p 4 + xb 74. sina 3p 4 - xb 75. sin1270° - u2 76. tan1180° + u2 77. tan12p - x2 78. sin1p + x2 Find cos1s + t2 and cos1s - t2. See Example 5. 79. sins = 3 5 and sint = - 12 13, s in quadrant I and t in quadrant III 80. cos s = - 8 17 and cos t = - 3 5, s and t in quadrant III 81. cos s = -1 5 and sint = 3 5, s and t in quadrant II 82. sins = 2 3 and sint = - 1 3, s in quadrant II and t in quadrant IV Use the given information to find (a) sin1s + t2, (b) tan1s + t2, and (c) the quadrant of s + t. See Example 5. 83. cos s = 3 5 and sint = 5 13, s and t in quadrant I 84. sins = 3 5 and sint = - 12 13, s in quadrant I and t in quadrant III 85. cos s = - 8 17 and cos t = - 3 5, s and t in quadrant III 86. cos s = -15 17 and sint = 4 5, s in quadrant II and t in quadrant I 87. sins = 2 3 and sint = - 1 3, s in quadrant II and t in quadrant IV 88. cos s = -1 5 and sint = 3 5, s and t in quadrant II Graph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verify your conjecture algebraically. 89. sina p 2 + ub 90. sina 3p 2 + ub 91. tana p 2 + ub 92. tana p 2 - ub Verify that each equation is an identity. See Example 7. 93. sin2x = 2 sinx cos x 1Hint: sin 2x = sin1x + x22 94. sin1x + y2 + sin1x - y2 = 2 sinx cos y 95. sina 7p 6 + xb - cos a 2p 3 + xb = 0 96. tan1x - y2 - tan1y - x2 = 21tanx - tany2 1 + tanx tany 97. cos1a - b2 cos asinb = tana + cot b 98. sin1s + t2 cos s cos t = tans + tant 99. sin1x - y2 sin1x + y2 = tanx - tany tanx + tany 100. sin1x + y2 cos1x - y2 = cot x + cot y 1 + cot x cot y 101. sin1s - t2 sint + cos1s - t2 cos t = sins sint cos t 102. tan1a + b2 - tanb 1 + tan1a + b2 tanb = tana
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