sin(7x)cos(4x)+sin(x)-cos(7x)sin(4x)+cos(x)=0

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Solution for sin(7x)cos(4x)+sin(x)-cos(7x)sin(4x)+cos(x)=0 equation:


Simplifying
sin(7x) * cos(4x) + sin(x) + -1cos(7x) * sin(4x) + cos(x) = 0

Remove parenthesis around (7x)
ins * 7x * cos(4x) + sin(x) + -1cos(7x) * sin(4x) + cos(x) = 0

Remove parenthesis around (4x)
ins * 7x * cos * 4x + sin(x) + -1cos(7x) * sin(4x) + cos(x) = 0

Reorder the terms for easier multiplication:
7 * 4ins * x * cos * x + sin(x) + -1cos(7x) * sin(4x) + cos(x) = 0

Multiply 7 * 4
28ins * x * cos * x + sin(x) + -1cos(7x) * sin(4x) + cos(x) = 0

Multiply ins * x
28insx * cos * x + sin(x) + -1cos(7x) * sin(4x) + cos(x) = 0

Multiply insx * cos
28cinos2x * x + sin(x) + -1cos(7x) * sin(4x) + cos(x) = 0

Multiply cinos2x * x
28cinos2x2 + sin(x) + -1cos(7x) * sin(4x) + cos(x) = 0

Multiply ins * x
28cinos2x2 + insx + -1cos(7x) * sin(4x) + cos(x) = 0

Remove parenthesis around (7x)
28cinos2x2 + insx + -1cos * 7x * sin(4x) + cos(x) = 0

Remove parenthesis around (4x)
28cinos2x2 + insx + -1cos * 7x * ins * 4x + cos(x) = 0

Reorder the terms for easier multiplication:
28cinos2x2 + insx + -1 * 7 * 4cos * x * ins * x + cos(x) = 0

Multiply -1 * 7
28cinos2x2 + insx + -7 * 4cos * x * ins * x + cos(x) = 0

Multiply -7 * 4
28cinos2x2 + insx + -28cos * x * ins * x + cos(x) = 0

Multiply cos * x
28cinos2x2 + insx + -28cosx * ins * x + cos(x) = 0

Multiply cosx * ins
28cinos2x2 + insx + -28cinos2x * x + cos(x) = 0

Multiply cinos2x * x
28cinos2x2 + insx + -28cinos2x2 + cos(x) = 0

Multiply cos * x
28cinos2x2 + insx + -28cinos2x2 + cosx = 0

Reorder the terms:
28cinos2x2 + -28cinos2x2 + cosx + insx = 0

Combine like terms: 28cinos2x2 + -28cinos2x2 = 0
0 + cosx + insx = 0
cosx + insx = 0

Solving
cosx + insx = 0

Solving for variable 'c'.

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

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

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

Divide each side by 'osx'.
c = -1ino-1

Simplifying
c = -1ino-1

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