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Simplifying Cos(x) + cos(2x) + cos(3x) + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0 Multiply osC * x osxC + cos(2x) + cos(3x) + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0 Remove parenthesis around (2x) osxC + cos * 2x + cos(3x) + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0 Reorder the terms for easier multiplication: osxC + 2cos * x + cos(3x) + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0 Multiply cos * x osxC + 2cosx + cos(3x) + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0 Remove parenthesis around (3x) osxC + 2cosx + cos * 3x + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0 Reorder the terms for easier multiplication: osxC + 2cosx + 3cos * x + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0 Multiply cos * x osxC + 2cosx + 3cosx + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0 Remove parenthesis around (4x) osxC + 2cosx + 3cosx + cos * 4x + cos(5x) + cos(6x) + cos(7x) = 0 Reorder the terms for easier multiplication: osxC + 2cosx + 3cosx + 4cos * x + cos(5x) + cos(6x) + cos(7x) = 0 Multiply cos * x osxC + 2cosx + 3cosx + 4cosx + cos(5x) + cos(6x) + cos(7x) = 0 Remove parenthesis around (5x) osxC + 2cosx + 3cosx + 4cosx + cos * 5x + cos(6x) + cos(7x) = 0 Reorder the terms for easier multiplication: osxC + 2cosx + 3cosx + 4cosx + 5cos * x + cos(6x) + cos(7x) = 0 Multiply cos * x osxC + 2cosx + 3cosx + 4cosx + 5cosx + cos(6x) + cos(7x) = 0 Remove parenthesis around (6x) osxC + 2cosx + 3cosx + 4cosx + 5cosx + cos * 6x + cos(7x) = 0 Reorder the terms for easier multiplication: osxC + 2cosx + 3cosx + 4cosx + 5cosx + 6cos * x + cos(7x) = 0 Multiply cos * x osxC + 2cosx + 3cosx + 4cosx + 5cosx + 6cosx + cos(7x) = 0 Remove parenthesis around (7x) osxC + 2cosx + 3cosx + 4cosx + 5cosx + 6cosx + cos * 7x = 0 Reorder the terms for easier multiplication: osxC + 2cosx + 3cosx + 4cosx + 5cosx + 6cosx + 7cos * x = 0 Multiply cos * x osxC + 2cosx + 3cosx + 4cosx + 5cosx + 6cosx + 7cosx = 0 Reorder the terms: 2cosx + 3cosx + 4cosx + 5cosx + 6cosx + 7cosx + osxC = 0 Combine like terms: 2cosx + 3cosx = 5cosx 5cosx + 4cosx + 5cosx + 6cosx + 7cosx + osxC = 0 Combine like terms: 5cosx + 4cosx = 9cosx 9cosx + 5cosx + 6cosx + 7cosx + osxC = 0 Combine like terms: 9cosx + 5cosx = 14cosx 14cosx + 6cosx + 7cosx + osxC = 0 Combine like terms: 14cosx + 6cosx = 20cosx 20cosx + 7cosx + osxC = 0 Combine like terms: 20cosx + 7cosx = 27cosx 27cosx + osxC = 0 Solving 27cosx + osxC = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1osxC' to each side of the equation. 27cosx + osxC + -1osxC = 0 + -1osxC Combine like terms: osxC + -1osxC = 0 27cosx + 0 = 0 + -1osxC 27cosx = 0 + -1osxC Remove the zero: 27cosx = -1osxC Divide each side by '27osx'. c = -0.03703703704C Simplifying c = -0.03703703704C
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