sin(3x+5)=cos(4x-10)

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Solution for sin(3x+5)=cos(4x-10) equation: 


Simplifying
sin(3x + 5) = cos(4x + -10)

Reorder the terms:
ins(5 + 3x) = cos(4x + -10)
(5 * ins + 3x * ins) = cos(4x + -10)
(5ins + 3insx) = cos(4x + -10)

Reorder the terms:
5ins + 3insx = cos(-10 + 4x)
5ins + 3insx = (-10 * cos + 4x * cos)
5ins + 3insx = (-10cos + 4cosx)

Solving
5ins + 3insx = -10cos + 4cosx

Solving for variable 'i'.

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

Reorder the terms:
10cos + -4cosx + 5ins + 3insx = -10cos + 4cosx + 10cos + -4cosx

Reorder the terms:
10cos + -4cosx + 5ins + 3insx = -10cos + 10cos + 4cosx + -4cosx

Combine like terms: -10cos + 10cos = 0
10cos + -4cosx + 5ins + 3insx = 0 + 4cosx + -4cosx
10cos + -4cosx + 5ins + 3insx = 4cosx + -4cosx

Combine like terms: 4cosx + -4cosx = 0
10cos + -4cosx + 5ins + 3insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(10co + -4cox + 5in + 3inx) = 0


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

Simplifying
s = 0

Solving
s = 0

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

Add '-1s' to each side of the equation.
s + -1s = 0 + -1s
Remove the zero:
0 = -1s

Simplifying
0 = -1s

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 + -4cox + 5in + 3inx)' equal to zero and attempt to solve:

Simplifying
10co + -4cox + 5in + 3inx = 0

Solving
10co + -4cox + 5in + 3inx = 0

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

Add '-10co' to each side of the equation.
10co + -4cox + 5in + -10co + 3inx = 0 + -10co

Reorder the terms:
10co + -10co + -4cox + 5in + 3inx = 0 + -10co

Combine like terms: 10co + -10co = 0
0 + -4cox + 5in + 3inx = 0 + -10co
-4cox + 5in + 3inx = 0 + -10co
Remove the zero:
-4cox + 5in + 3inx = -10co

Add '4cox' to each side of the equation.
-4cox + 5in + 4cox + 3inx = -10co + 4cox

Reorder the terms:
-4cox + 4cox + 5in + 3inx = -10co + 4cox

Combine like terms: -4cox + 4cox = 0
0 + 5in + 3inx = -10co + 4cox
5in + 3inx = -10co + 4cox

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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