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Simplifying cos(x) + cos(2x) + cos(3x) + cos(4x) + cos(5x) + cos(6x) = 0 Multiply cos * x cosx + cos(2x) + cos(3x) + cos(4x) + cos(5x) + cos(6x) = 0 Remove parenthesis around (2x) cosx + cos * 2x + cos(3x) + cos(4x) + cos(5x) + cos(6x) = 0 Reorder the terms for easier multiplication: cosx + 2cos * x + cos(3x) + cos(4x) + cos(5x) + cos(6x) = 0 Multiply cos * x cosx + 2cosx + cos(3x) + cos(4x) + cos(5x) + cos(6x) = 0 Remove parenthesis around (3x) cosx + 2cosx + cos * 3x + cos(4x) + cos(5x) + cos(6x) = 0 Reorder the terms for easier multiplication: cosx + 2cosx + 3cos * x + cos(4x) + cos(5x) + cos(6x) = 0 Multiply cos * x cosx + 2cosx + 3cosx + cos(4x) + cos(5x) + cos(6x) = 0 Remove parenthesis around (4x) cosx + 2cosx + 3cosx + cos * 4x + cos(5x) + cos(6x) = 0 Reorder the terms for easier multiplication: cosx + 2cosx + 3cosx + 4cos * x + cos(5x) + cos(6x) = 0 Multiply cos * x cosx + 2cosx + 3cosx + 4cosx + cos(5x) + cos(6x) = 0 Remove parenthesis around (5x) cosx + 2cosx + 3cosx + 4cosx + cos * 5x + cos(6x) = 0 Reorder the terms for easier multiplication: cosx + 2cosx + 3cosx + 4cosx + 5cos * x + cos(6x) = 0 Multiply cos * x cosx + 2cosx + 3cosx + 4cosx + 5cosx + cos(6x) = 0 Remove parenthesis around (6x) cosx + 2cosx + 3cosx + 4cosx + 5cosx + cos * 6x = 0 Reorder the terms for easier multiplication: cosx + 2cosx + 3cosx + 4cosx + 5cosx + 6cos * x = 0 Multiply cos * x cosx + 2cosx + 3cosx + 4cosx + 5cosx + 6cosx = 0 Combine like terms: cosx + 2cosx = 3cosx 3cosx + 3cosx + 4cosx + 5cosx + 6cosx = 0 Combine like terms: 3cosx + 3cosx = 6cosx 6cosx + 4cosx + 5cosx + 6cosx = 0 Combine like terms: 6cosx + 4cosx = 10cosx 10cosx + 5cosx + 6cosx = 0 Combine like terms: 10cosx + 5cosx = 15cosx 15cosx + 6cosx = 0 Combine like terms: 15cosx + 6cosx = 21cosx 21cosx = 0 Solving 21cosx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Divide each side by '21'. cosx = 0 Simplifying cosx = 0 The solution to this equation could not be determined.
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