cos(5x)cos(2x)+cos(5x)sin(2x)=0

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Solution for cos(5x)cos(2x)+cos(5x)sin(2x)=0 equation: 


Simplifying
cos(5x) * cos(2x) + cos(5x) * sin(2x) = 0

Remove parenthesis around (5x)
cos * 5x * cos(2x) + cos(5x) * sin(2x) = 0

Remove parenthesis around (2x)
cos * 5x * cos * 2x + cos(5x) * sin(2x) = 0

Reorder the terms for easier multiplication:
5 * 2cos * x * cos * x + cos(5x) * sin(2x) = 0

Multiply 5 * 2
10cos * x * cos * x + cos(5x) * sin(2x) = 0

Multiply cos * x
10cosx * cos * x + cos(5x) * sin(2x) = 0

Multiply cosx * cos
10c2o2s2x * x + cos(5x) * sin(2x) = 0

Multiply c2o2s2x * x
10c2o2s2x2 + cos(5x) * sin(2x) = 0

Remove parenthesis around (5x)
10c2o2s2x2 + cos * 5x * sin(2x) = 0

Remove parenthesis around (2x)
10c2o2s2x2 + cos * 5x * ins * 2x = 0

Reorder the terms for easier multiplication:
10c2o2s2x2 + 5 * 2cos * x * ins * x = 0

Multiply 5 * 2
10c2o2s2x2 + 10cos * x * ins * x = 0

Multiply cos * x
10c2o2s2x2 + 10cosx * ins * x = 0

Multiply cosx * ins
10c2o2s2x2 + 10cinos2x * x = 0

Multiply cinos2x * x
10c2o2s2x2 + 10cinos2x2 = 0

Reorder the terms:
10cinos2x2 + 10c2o2s2x2 = 0

Solving
10cinos2x2 + 10c2o2s2x2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '10cos2x2'.
10cos2x2(in + co) = 0

Ignore the factor 10.

Subproblem 1
Set the factor 'cos2x2' equal to zero and attempt to solve:

Simplifying
cos2x2 = 0

Solving
cos2x2 = 0

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

Simplifying
cos2x2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(in + co)' equal to zero and attempt to solve:

Simplifying
in + co = 0

Reorder the terms:
co + in = 0

Solving
co + in = 0

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

Add '-1in' to each side of the equation.
co + in + -1in = 0 + -1in

Combine like terms: in + -1in = 0
co + 0 = 0 + -1in
co = 0 + -1in
Remove the zero:
co = -1in

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

Simplifying
c = -1ino-1
Solution
c = {-1ino-1}

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