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Cos 3.x - cos 7x 53. sin 7x + sin 3.x cos tan 2r 54. sin = %3D

Cos 3.x - cos 7x 53. sin 7x + sin 3.x cos tan 2r 54. sin = %3D

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 23E
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Solve number 53
49. 72. cc In Exercises 51-60, verify each identity. sin 2r + sin 4x 52. cos 2r + cos 4x 73. sin x + sin 3x 51. COS x + cos 3.r = tan 3.x SI = tan 2r cos 12r – cos 4x 54. sin 4x - sin 12r 74. cos 3x - cos 7x 53. sin 7x + sin 3.r tan 8x %3D = tan 2r 75. cos 2r + cos 2y 55. cos 2r- cos 2y = cot (y- x) cot (y + x) tan (x + y) 76. sin 2r + sin 2y 56. sin 2r sin 2y tan (x - y) 77. 57. sin x + sin 2r + sin 3x = sin 2r(1 + 2 cos x) 58. cos x + cos 2r + cos 3x = cos 2r(1 + 2 cos x) 59. sin 2x + sin 4x + sin 6x = 4 cos x cos 2r sin 3x 78. 60. cos x + cos 3x + cos 5x + cos 7x = 4 cos.x cos 2r cos 4x Applying the Concepts
Transcribed Image Text:49. 72. cc In Exercises 51-60, verify each identity. sin 2r + sin 4x 52. cos 2r + cos 4x 73. sin x + sin 3x 51. COS x + cos 3.r = tan 3.x SI = tan 2r cos 12r – cos 4x 54. sin 4x - sin 12r 74. cos 3x - cos 7x 53. sin 7x + sin 3.r tan 8x %3D = tan 2r 75. cos 2r + cos 2y 55. cos 2r- cos 2y = cot (y- x) cot (y + x) tan (x + y) 76. sin 2r + sin 2y 56. sin 2r sin 2y tan (x - y) 77. 57. sin x + sin 2r + sin 3x = sin 2r(1 + 2 cos x) 58. cos x + cos 2r + cos 3x = cos 2r(1 + 2 cos x) 59. sin 2x + sin 4x + sin 6x = 4 cos x cos 2r sin 3x 78. 60. cos x + cos 3x + cos 5x + cos 7x = 4 cos.x cos 2r cos 4x Applying the Concepts
1/2 cos(-8) = cose cos(28) = CUS U 1+ cos tan(-0) = - tan 6 = 2 cos?e - 1 cos csc(-6) = – csce = 1- 2 sin? 0 %3D cos 8 sec(-0) = sec 0 2 tan e %3D tan(28) tan = + + cos 6 1- tan? e cot(-6) = - cote PRODUCT TO SUM IDENTITIES SUM TO PRODUCT IDENTITIES sin a sin ß = [cos (a - B) - cos(a + B)] sin a + sin ß = 2 sin a +B CoS cos a cos ß =5 [cos (a - B) + cos(a +B)] sin a – sin B = 2 cos a +B sin 1 sin a cos B = [sin(a +B) + sin(a - B)] a+ B %3D cos a + cos B = 2 cos CoS cos a sin ß =, (sin(a +B) – sin(a- B)] cos a - cos ß = -2 sin (")sin (",) a+B SUM/DIFFERENCES IDENTITIES MOLLWEIDE'S FORMULA sin (a ±B) = sin a cos B ±cosa sin B cos(a – B)l
Transcribed Image Text:1/2 cos(-8) = cose cos(28) = CUS U 1+ cos tan(-0) = - tan 6 = 2 cos?e - 1 cos csc(-6) = – csce = 1- 2 sin? 0 %3D cos 8 sec(-0) = sec 0 2 tan e %3D tan(28) tan = + + cos 6 1- tan? e cot(-6) = - cote PRODUCT TO SUM IDENTITIES SUM TO PRODUCT IDENTITIES sin a sin ß = [cos (a - B) - cos(a + B)] sin a + sin ß = 2 sin a +B CoS cos a cos ß =5 [cos (a - B) + cos(a +B)] sin a – sin B = 2 cos a +B sin 1 sin a cos B = [sin(a +B) + sin(a - B)] a+ B %3D cos a + cos B = 2 cos CoS cos a sin ß =, (sin(a +B) – sin(a- B)] cos a - cos ß = -2 sin (")sin (",) a+B SUM/DIFFERENCES IDENTITIES MOLLWEIDE'S FORMULA sin (a ±B) = sin a cos B ±cosa sin B cos(a – B)l
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