Question

Solve cos 3x - cos 4x = cos 5x - cos 6x.

Answer 1

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

Answer 2

Step-by-step explanation:

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