sin(2x)*sin(3x)=cos(5x)*sin(4x)

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Solution for sin(2x)*sin(3x)=cos(5x)*sin(4x) equation: 


Simplifying
sin(2x) * sin(3x) = cos(5x) * sin(4x)

Remove parenthesis around (2x)
ins * 2x * sin(3x) = cos(5x) * sin(4x)

Remove parenthesis around (3x)
ins * 2x * ins * 3x = cos(5x) * sin(4x)

Reorder the terms for easier multiplication:
2 * 3ins * x * ins * x = cos(5x) * sin(4x)

Multiply 2 * 3
6ins * x * ins * x = cos(5x) * sin(4x)

Multiply ins * x
6insx * ins * x = cos(5x) * sin(4x)

Multiply insx * ins
6i2n2s2x * x = cos(5x) * sin(4x)

Multiply i2n2s2x * x
6i2n2s2x2 = cos(5x) * sin(4x)

Remove parenthesis around (5x)
6i2n2s2x2 = cos * 5x * sin(4x)

Remove parenthesis around (4x)
6i2n2s2x2 = cos * 5x * ins * 4x

Reorder the terms for easier multiplication:
6i2n2s2x2 = 5 * 4cos * x * ins * x

Multiply 5 * 4
6i2n2s2x2 = 20cos * x * ins * x

Multiply cos * x
6i2n2s2x2 = 20cosx * ins * x

Multiply cosx * ins
6i2n2s2x2 = 20cinos2x * x

Multiply cinos2x * x
6i2n2s2x2 = 20cinos2x2

Solving
6i2n2s2x2 = 20cinos2x2

Solving for variable 'i'.

Reorder the terms:
-20cinos2x2 + 6i2n2s2x2 = 20cinos2x2 + -20cinos2x2

Combine like terms: 20cinos2x2 + -20cinos2x2 = 0
-20cinos2x2 + 6i2n2s2x2 = 0

Factor out the Greatest Common Factor (GCF), '2ins2x2'.
2ins2x2(-10co + 3in) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'ins2x2' equal to zero and attempt to solve:

Simplifying
ins2x2 = 0

Solving
ins2x2 = 0

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

Simplifying
ins2x2 = 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 '(-10co + 3in)' equal to zero and attempt to solve:

Simplifying
-10co + 3in = 0

Solving
-10co + 3in = 0

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

Add '10co' to each side of the equation.
-10co + 10co + 3in = 0 + 10co

Combine like terms: -10co + 10co = 0
0 + 3in = 0 + 10co
3in = 0 + 10co
Remove the zero:
3in = 10co

Divide each side by '3n'.
i = 3.333333333cn-1o

Simplifying
i = 3.333333333cn-1o
Solution
i = {3.333333333cn-1o}

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