sin(3x-20)=cos(3y+20)

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Solution for sin(3x-20)=cos(3y+20) equation:


Simplifying
sin(3x + -20) = cos(3y + 20)

Reorder the terms:
ins(-20 + 3x) = cos(3y + 20)
(-20 * ins + 3x * ins) = cos(3y + 20)
(-20ins + 3insx) = cos(3y + 20)

Reorder the terms:
-20ins + 3insx = cos(20 + 3y)
-20ins + 3insx = (20 * cos + 3y * cos)
-20ins + 3insx = (20cos + 3cosy)

Solving
-20ins + 3insx = 20cos + 3cosy

Solving for variable 'i'.

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

Reorder the terms:
-20cos + -3cosy + -20ins + 3insx = 20cos + 3cosy + -20cos + -3cosy

Reorder the terms:
-20cos + -3cosy + -20ins + 3insx = 20cos + -20cos + 3cosy + -3cosy

Combine like terms: 20cos + -20cos = 0
-20cos + -3cosy + -20ins + 3insx = 0 + 3cosy + -3cosy
-20cos + -3cosy + -20ins + 3insx = 3cosy + -3cosy

Combine like terms: 3cosy + -3cosy = 0
-20cos + -3cosy + -20ins + 3insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-20co + -3coy + -20in + 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 '(-20co + -3coy + -20in + 3inx)' equal to zero and attempt to solve: Simplifying -20co + -3coy + -20in + 3inx = 0 Solving -20co + -3coy + -20in + 3inx = 0 Move all terms containing i to the left, all other terms to the right. Add '20co' to each side of the equation. -20co + -3coy + -20in + 20co + 3inx = 0 + 20co Reorder the terms: -20co + 20co + -3coy + -20in + 3inx = 0 + 20co Combine like terms: -20co + 20co = 0 0 + -3coy + -20in + 3inx = 0 + 20co -3coy + -20in + 3inx = 0 + 20co Remove the zero: -3coy + -20in + 3inx = 20co Add '3coy' to each side of the equation. -3coy + -20in + 3coy + 3inx = 20co + 3coy Reorder the terms: -3coy + 3coy + -20in + 3inx = 20co + 3coy Combine like terms: -3coy + 3coy = 0 0 + -20in + 3inx = 20co + 3coy -20in + 3inx = 20co + 3coy 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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