61. sin a cos 3 60. cos (a + B) + cos (a - B) - 2 cos a cos B cos (a + B) 63. - tan a tan B sin (a + B) 62. cos a cos B - tan a + tan B cos a cos B sin (a + B) 65. sin (a- B) tan a + tan B cos (a - B) 64. - cot a + tan B tan a - tan B sin a cos B cot a cot B -1 cos (a + B) 66. cos (a - B) 1- tan a tan B 67. cot (a + B) cot B + cot a 1 + tan a tan B cot a cot B + 1 cot B csc a csc B cot a cot B-1 69. sec(a + B) 68. cot (a - B) %3D cot a sec a sec B 71. sin (a - B) sin (a + B) = sin a - sin? e 70. sec(a - B) 1+ tan a tan B sin B 73. sin (0 + km) = (-1) sin 0, k any integer 72. cos (a - B) cos (a + B) cos a 74. cos (0 + ka) = (-1) cos 0, k any integer In Problems 75-86, find the exact value of each expression. 75. sin sin 76. sin( sin- V3 + cos1) \ 77. sin sin 3 cos + cos 2 5 13) 78. sin sin tan 79. cos tan + cos 80. cos tan sin 12 12 + cos 13 83. tan sin+) 81. cos sin tan 13 4 82. cos tan 3 5 85. tan sin 4. + cos 84. tan cos 86. tan + sin In Problems 87-92, write each trigonometric expression as an algebraic expression containing u and v. Give the restrictions on u and v. 87. cos (cosu + sin v) -1 88. sin (sin u - cos v) 89. sin (tanu – sin" v) 90. cos (tan u + tan v) 91. tan (sinu - cos v) 92. sec (tanu + cos" v) In Problems 93-98, solve each equation on the interval 0 se < 27. 93. sin 0 - V3 cos 0 1 94. V3 sin 0 + cos 0 = 1 %3D 95. sin e + cos 0 = V2 96. sin 0 – cos 0 = -V2 97. tan 0 + V3 = sec 0 98. cot 0 + csc 0 = -V3 %3D %3! Applications and Extensions 99. Show that sin (sin v + cos v) = 1. 100. Show that cos (sin v + cos v) = 0. A 101. Calculus Show that the difference quotient for f(x) = sin x 103. One, Two, Three (a) Show that tan ( tan1 + tan12 + tan" 3) (b) Conclude from part (a) that 43
61. sin a cos 3 60. cos (a + B) + cos (a - B) - 2 cos a cos B cos (a + B) 63. - tan a tan B sin (a + B) 62. cos a cos B - tan a + tan B cos a cos B sin (a + B) 65. sin (a- B) tan a + tan B cos (a - B) 64. - cot a + tan B tan a - tan B sin a cos B cot a cot B -1 cos (a + B) 66. cos (a - B) 1- tan a tan B 67. cot (a + B) cot B + cot a 1 + tan a tan B cot a cot B + 1 cot B csc a csc B cot a cot B-1 69. sec(a + B) 68. cot (a - B) %3D cot a sec a sec B 71. sin (a - B) sin (a + B) = sin a - sin? e 70. sec(a - B) 1+ tan a tan B sin B 73. sin (0 + km) = (-1) sin 0, k any integer 72. cos (a - B) cos (a + B) cos a 74. cos (0 + ka) = (-1) cos 0, k any integer In Problems 75-86, find the exact value of each expression. 75. sin sin 76. sin( sin- V3 + cos1) \ 77. sin sin 3 cos + cos 2 5 13) 78. sin sin tan 79. cos tan + cos 80. cos tan sin 12 12 + cos 13 83. tan sin+) 81. cos sin tan 13 4 82. cos tan 3 5 85. tan sin 4. + cos 84. tan cos 86. tan + sin In Problems 87-92, write each trigonometric expression as an algebraic expression containing u and v. Give the restrictions on u and v. 87. cos (cosu + sin v) -1 88. sin (sin u - cos v) 89. sin (tanu – sin" v) 90. cos (tan u + tan v) 91. tan (sinu - cos v) 92. sec (tanu + cos" v) In Problems 93-98, solve each equation on the interval 0 se < 27. 93. sin 0 - V3 cos 0 1 94. V3 sin 0 + cos 0 = 1 %3D 95. sin e + cos 0 = V2 96. sin 0 – cos 0 = -V2 97. tan 0 + V3 = sec 0 98. cot 0 + csc 0 = -V3 %3D %3! Applications and Extensions 99. Show that sin (sin v + cos v) = 1. 100. Show that cos (sin v + cos v) = 0. A 101. Calculus Show that the difference quotient for f(x) = sin x 103. One, Two, Three (a) Show that tan ( tan1 + tan12 + tan" 3) (b) Conclude from part (a) that 43
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 59E
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