1+cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x)+cos(6x)+cos(7x)=0

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Solution for 1+cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x)+cos(6x)+cos(7x)=0 equation:


Simplifying
1 + cos(x) + cos(2x) + cos(3x) + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0

Multiply cos * x
1 + cosx + cos(2x) + cos(3x) + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0

Remove parenthesis around (2x)
1 + cosx + cos * 2x + cos(3x) + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0

Reorder the terms for easier multiplication:
1 + cosx + 2cos * x + cos(3x) + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0

Multiply cos * x
1 + cosx + 2cosx + cos(3x) + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0

Remove parenthesis around (3x)
1 + cosx + 2cosx + cos * 3x + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0

Reorder the terms for easier multiplication:
1 + cosx + 2cosx + 3cos * x + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0

Multiply cos * x
1 + cosx + 2cosx + 3cosx + cos(4x) + cos(5x) + cos(6x) + cos(7x) = 0

Remove parenthesis around (4x)
1 + cosx + 2cosx + 3cosx + cos * 4x + cos(5x) + cos(6x) + cos(7x) = 0

Reorder the terms for easier multiplication:
1 + cosx + 2cosx + 3cosx + 4cos * x + cos(5x) + cos(6x) + cos(7x) = 0

Multiply cos * x
1 + cosx + 2cosx + 3cosx + 4cosx + cos(5x) + cos(6x) + cos(7x) = 0

Remove parenthesis around (5x)
1 + cosx + 2cosx + 3cosx + 4cosx + cos * 5x + cos(6x) + cos(7x) = 0

Reorder the terms for easier multiplication:
1 + cosx + 2cosx + 3cosx + 4cosx + 5cos * x + cos(6x) + cos(7x) = 0

Multiply cos * x
1 + cosx + 2cosx + 3cosx + 4cosx + 5cosx + cos(6x) + cos(7x) = 0

Remove parenthesis around (6x)
1 + cosx + 2cosx + 3cosx + 4cosx + 5cosx + cos * 6x + cos(7x) = 0

Reorder the terms for easier multiplication:
1 + cosx + 2cosx + 3cosx + 4cosx + 5cosx + 6cos * x + cos(7x) = 0

Multiply cos * x
1 + cosx + 2cosx + 3cosx + 4cosx + 5cosx + 6cosx + cos(7x) = 0

Remove parenthesis around (7x)
1 + cosx + 2cosx + 3cosx + 4cosx + 5cosx + 6cosx + cos * 7x = 0

Reorder the terms for easier multiplication:
1 + cosx + 2cosx + 3cosx + 4cosx + 5cosx + 6cosx + 7cos * x = 0

Multiply cos * x
1 + cosx + 2cosx + 3cosx + 4cosx + 5cosx + 6cosx + 7cosx = 0

Combine like terms: cosx + 2cosx = 3cosx
1 + 3cosx + 3cosx + 4cosx + 5cosx + 6cosx + 7cosx = 0

Combine like terms: 3cosx + 3cosx = 6cosx
1 + 6cosx + 4cosx + 5cosx + 6cosx + 7cosx = 0

Combine like terms: 6cosx + 4cosx = 10cosx
1 + 10cosx + 5cosx + 6cosx + 7cosx = 0

Combine like terms: 10cosx + 5cosx = 15cosx
1 + 15cosx + 6cosx + 7cosx = 0

Combine like terms: 15cosx + 6cosx = 21cosx
1 + 21cosx + 7cosx = 0

Combine like terms: 21cosx + 7cosx = 28cosx
1 + 28cosx = 0

Solving
1 + 28cosx = 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 + 28cosx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 28cosx = 0 + -1
28cosx = 0 + -1

Combine like terms: 0 + -1 = -1
28cosx = -1

Divide each side by '28osx'.
c = -0.03571428571o-1s-1x-1

Simplifying
c = -0.03571428571o-1s-1x-1

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