sin(3x+5)=cos(4x+1)

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Solution for sin(3x+5)=cos(4x+1) equation:


Simplifying
sin(3x + 5) = cos(4x + 1)

Reorder the terms:
ins(5 + 3x) = cos(4x + 1)
(5 * ins + 3x * ins) = cos(4x + 1)
(5ins + 3insx) = cos(4x + 1)

Reorder the terms:
5ins + 3insx = cos(1 + 4x)
5ins + 3insx = (1 * cos + 4x * cos)
5ins + 3insx = (1cos + 4cosx)

Solving
5ins + 3insx = 1cos + 4cosx

Solving for variable 'i'.

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

Reorder the terms:
-1cos + -4cosx + 5ins + 3insx = 1cos + 4cosx + -1cos + -4cosx

Reorder the terms:
-1cos + -4cosx + 5ins + 3insx = 1cos + -1cos + 4cosx + -4cosx

Combine like terms: 1cos + -1cos = 0
-1cos + -4cosx + 5ins + 3insx = 0 + 4cosx + -4cosx
-1cos + -4cosx + 5ins + 3insx = 4cosx + -4cosx

Combine like terms: 4cosx + -4cosx = 0
-1cos + -4cosx + 5ins + 3insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-1co + -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 '(-1co + -4cox + 5in + 3inx)' equal to zero and attempt to solve: Simplifying -1co + -4cox + 5in + 3inx = 0 Solving -1co + -4cox + 5in + 3inx = 0 Move all terms containing i to the left, all other terms to the right. Add 'co' to each side of the equation. -1co + -4cox + 5in + co + 3inx = 0 + co Reorder the terms: -1co + co + -4cox + 5in + 3inx = 0 + co Combine like terms: -1co + co = 0 0 + -4cox + 5in + 3inx = 0 + co -4cox + 5in + 3inx = 0 + co Remove the zero: -4cox + 5in + 3inx = co Add '4cox' to each side of the equation. -4cox + 5in + 4cox + 3inx = co + 4cox Reorder the terms: -4cox + 4cox + 5in + 3inx = co + 4cox Combine like terms: -4cox + 4cox = 0 0 + 5in + 3inx = co + 4cox 5in + 3inx = co + 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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