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Simplifying cos(x) + cos(2x) + cos(3x) + cos(4x) + 1 = 0 Multiply cos * x cosx + cos(2x) + cos(3x) + cos(4x) + 1 = 0 Remove parenthesis around (2x) cosx + cos * 2x + cos(3x) + cos(4x) + 1 = 0 Reorder the terms for easier multiplication: cosx + 2cos * x + cos(3x) + cos(4x) + 1 = 0 Multiply cos * x cosx + 2cosx + cos(3x) + cos(4x) + 1 = 0 Remove parenthesis around (3x) cosx + 2cosx + cos * 3x + cos(4x) + 1 = 0 Reorder the terms for easier multiplication: cosx + 2cosx + 3cos * x + cos(4x) + 1 = 0 Multiply cos * x cosx + 2cosx + 3cosx + cos(4x) + 1 = 0 Remove parenthesis around (4x) cosx + 2cosx + 3cosx + cos * 4x + 1 = 0 Reorder the terms for easier multiplication: cosx + 2cosx + 3cosx + 4cos * x + 1 = 0 Multiply cos * x cosx + 2cosx + 3cosx + 4cosx + 1 = 0 Reorder the terms: 1 + cosx + 2cosx + 3cosx + 4cosx = 0 Combine like terms: cosx + 2cosx = 3cosx 1 + 3cosx + 3cosx + 4cosx = 0 Combine like terms: 3cosx + 3cosx = 6cosx 1 + 6cosx + 4cosx = 0 Combine like terms: 6cosx + 4cosx = 10cosx 1 + 10cosx = 0 Solving 1 + 10cosx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 10cosx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 10cosx = 0 + -1 10cosx = 0 + -1 Combine like terms: 0 + -1 = -1 10cosx = -1 Divide each side by '10osx'. c = -0.1o-1s-1x-1 Simplifying c = -0.1o-1s-1x-1
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