Cos(3x)-cos(7x)=cos(x)-cos(7x)

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Solution for Cos(3x)-cos(7x)=cos(x)-cos(7x) equation:


Simplifying
Cos(3x) + -1cos(7x) = cos(x) + -1cos(7x)

Remove parenthesis around (3x)
osC * 3x + -1cos(7x) = cos(x) + -1cos(7x)

Reorder the terms for easier multiplication:
3osC * x + -1cos(7x) = cos(x) + -1cos(7x)

Multiply osC * x
3osxC + -1cos(7x) = cos(x) + -1cos(7x)

Remove parenthesis around (7x)
3osxC + -1cos * 7x = cos(x) + -1cos(7x)

Reorder the terms for easier multiplication:
3osxC + -1 * 7cos * x = cos(x) + -1cos(7x)

Multiply -1 * 7
3osxC + -7cos * x = cos(x) + -1cos(7x)

Multiply cos * x
3osxC + -7cosx = cos(x) + -1cos(7x)

Reorder the terms:
-7cosx + 3osxC = cos(x) + -1cos(7x)

Multiply cos * x
-7cosx + 3osxC = cosx + -1cos(7x)

Remove parenthesis around (7x)
-7cosx + 3osxC = cosx + -1cos * 7x

Reorder the terms for easier multiplication:
-7cosx + 3osxC = cosx + -1 * 7cos * x

Multiply -1 * 7
-7cosx + 3osxC = cosx + -7cos * x

Multiply cos * x
-7cosx + 3osxC = cosx + -7cosx

Combine like terms: cosx + -7cosx = -6cosx
-7cosx + 3osxC = -6cosx

Solving
-7cosx + 3osxC = -6cosx

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '6cosx' to each side of the equation.
-7cosx + 6cosx + 3osxC = -6cosx + 6cosx

Combine like terms: -7cosx + 6cosx = -1cosx
-1cosx + 3osxC = -6cosx + 6cosx

Combine like terms: -6cosx + 6cosx = 0
-1cosx + 3osxC = 0

Add '-3osxC' to each side of the equation.
-1cosx + 3osxC + -3osxC = 0 + -3osxC

Combine like terms: 3osxC + -3osxC = 0
-1cosx + 0 = 0 + -3osxC
-1cosx = 0 + -3osxC
Remove the zero:
-1cosx = -3osxC

Divide each side by '-1osx'.
c = 3C

Simplifying
c = 3C

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