sin(x+9)=cos(x+5)

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Solution for sin(x+9)=cos(x+5) equation:


Simplifying
sin(x + 9) = cos(x + 5)

Reorder the terms:
ins(9 + x) = cos(x + 5)
(9 * ins + x * ins) = cos(x + 5)
(9ins + insx) = cos(x + 5)

Reorder the terms:
9ins + insx = cos(5 + x)
9ins + insx = (5 * cos + x * cos)
9ins + insx = (5cos + cosx)

Solving
9ins + insx = 5cos + cosx

Solving for variable 'i'.

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

Reorder the terms:
-5cos + -1cosx + 9ins + insx = 5cos + cosx + -5cos + -1cosx

Reorder the terms:
-5cos + -1cosx + 9ins + insx = 5cos + -5cos + cosx + -1cosx

Combine like terms: 5cos + -5cos = 0
-5cos + -1cosx + 9ins + insx = 0 + cosx + -1cosx
-5cos + -1cosx + 9ins + insx = cosx + -1cosx

Combine like terms: cosx + -1cosx = 0
-5cos + -1cosx + 9ins + insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-5co + -1cox + 9in + inx) = 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 '(-5co + -1cox + 9in + inx)' equal to zero and attempt to solve: Simplifying -5co + -1cox + 9in + inx = 0 Solving -5co + -1cox + 9in + inx = 0 Move all terms containing i to the left, all other terms to the right. Add '5co' to each side of the equation. -5co + -1cox + 9in + 5co + inx = 0 + 5co Reorder the terms: -5co + 5co + -1cox + 9in + inx = 0 + 5co Combine like terms: -5co + 5co = 0 0 + -1cox + 9in + inx = 0 + 5co -1cox + 9in + inx = 0 + 5co Remove the zero: -1cox + 9in + inx = 5co Add 'cox' to each side of the equation. -1cox + 9in + cox + inx = 5co + cox Reorder the terms: -1cox + cox + 9in + inx = 5co + cox Combine like terms: -1cox + cox = 0 0 + 9in + inx = 5co + cox 9in + inx = 5co + cox 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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