Solve cos 3x - cos 4x = cos 5x - cos 6x.
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Answer: x = 0 , x = 2π/9 And x = 2π
For General Solution: Add 2nπ to all the answers.
Given that
cos 3x - cos 4x = cos 5x - cos 6x
cos 6x - cos 4x = cos 5x - cos 3x
- 2 sin[(6x + 4x)/2].sin[(6x - 4x)/2] = - 2 sin[(5x + 3x)/2].sin[(5x - 3x)/2]
sin[(10x)/2].sin[(2x)/2] = sin[(8x)/2].sin[(2x)/2]
sin 5x . sin x = sin 4x . sin x
sin 5x = sin 4x
sin 5x - sin 4x = 0
2 cos[(5x + 4x)/2].sin[(5x - 4x)/2] = 0
sin (9x/2) . sin x/2 = 0
sin (9x/2) = 0 ; sin x/2 = 0
For sin (9x/2) = 0 :
sin (9x/2) = 0
9x/2 = 0 AND 9x/2 = π
x = 0 AND x = 2π/9
For sin x/2 = 0 :
sin x/2 = 0
x/2 = 0 AND x/2 = π
x = 0 AND x = 2π
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