cos(5x-4)=sin(8x+18)

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Solution for cos(5x-4)=sin(8x+18) equation:


Simplifying
cos(5x + -4) = sin(8x + 18)

Reorder the terms:
cos(-4 + 5x) = sin(8x + 18)
(-4 * cos + 5x * cos) = sin(8x + 18)
(-4cos + 5cosx) = sin(8x + 18)

Reorder the terms:
-4cos + 5cosx = ins(18 + 8x)
-4cos + 5cosx = (18 * ins + 8x * ins)
-4cos + 5cosx = (18ins + 8insx)

Solving
-4cos + 5cosx = 18ins + 8insx

Solving for variable 'c'.

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

Reorder the terms:
-4cos + 5cosx + -18ins + -8insx = 18ins + -18ins + 8insx + -8insx

Combine like terms: 18ins + -18ins = 0
-4cos + 5cosx + -18ins + -8insx = 0 + 8insx + -8insx
-4cos + 5cosx + -18ins + -8insx = 8insx + -8insx

Combine like terms: 8insx + -8insx = 0
-4cos + 5cosx + -18ins + -8insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-4co + 5cox + -18in + -8inx) = 0

Subproblem 1

Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing c 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 '(-4co + 5cox + -18in + -8inx)' equal to zero and attempt to solve: Simplifying -4co + 5cox + -18in + -8inx = 0 Solving -4co + 5cox + -18in + -8inx = 0 Move all terms containing c to the left, all other terms to the right. Add '18in' to each side of the equation. -4co + 5cox + -18in + 18in + -8inx = 0 + 18in Combine like terms: -18in + 18in = 0 -4co + 5cox + 0 + -8inx = 0 + 18in -4co + 5cox + -8inx = 0 + 18in Remove the zero: -4co + 5cox + -8inx = 18in Add '8inx' to each side of the equation. -4co + 5cox + -8inx + 8inx = 18in + 8inx Combine like terms: -8inx + 8inx = 0 -4co + 5cox + 0 = 18in + 8inx -4co + 5cox = 18in + 8inx 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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