cos(3x-60)-sin(3x-60)=0

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Solution for cos(3x-60)-sin(3x-60)=0 equation:


Simplifying
cos(3x + -60) + -1sin(3x + -60) = 0

Reorder the terms:
cos(-60 + 3x) + -1sin(3x + -60) = 0
(-60 * cos + 3x * cos) + -1sin(3x + -60) = 0
(-60cos + 3cosx) + -1sin(3x + -60) = 0

Reorder the terms:
-60cos + 3cosx + -1ins(-60 + 3x) = 0
-60cos + 3cosx + (-60 * -1ins + 3x * -1ins) = 0
-60cos + 3cosx + (60ins + -3insx) = 0

Solving
-60cos + 3cosx + 60ins + -3insx = 0

Solving for variable 'c'.

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

Add '-60ins' to each side of the equation.
-60cos + 3cosx + 60ins + -60ins + -3insx = 0 + -60ins

Combine like terms: 60ins + -60ins = 0
-60cos + 3cosx + 0 + -3insx = 0 + -60ins
-60cos + 3cosx + -3insx = 0 + -60ins
Remove the zero:
-60cos + 3cosx + -3insx = -60ins

Add '3insx' to each side of the equation.
-60cos + 3cosx + -3insx + 3insx = -60ins + 3insx

Combine like terms: -3insx + 3insx = 0
-60cos + 3cosx + 0 = -60ins + 3insx
-60cos + 3cosx = -60ins + 3insx

Reorder the terms:
-60cos + 3cosx + 60ins + -3insx = -60ins + 60ins + 3insx + -3insx

Combine like terms: -60ins + 60ins = 0
-60cos + 3cosx + 60ins + -3insx = 0 + 3insx + -3insx
-60cos + 3cosx + 60ins + -3insx = 3insx + -3insx

Combine like terms: 3insx + -3insx = 0
-60cos + 3cosx + 60ins + -3insx = 0

Factor out the Greatest Common Factor (GCF), '3s'.
3s(-20co + cox + 20in + -1inx) = 0

Ignore the factor 3.

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 '(-20co + cox + 20in + -1inx)' equal to zero and attempt to solve: Simplifying -20co + cox + 20in + -1inx = 0 Solving -20co + cox + 20in + -1inx = 0 Move all terms containing c to the left, all other terms to the right. Add '-20in' to each side of the equation. -20co + cox + 20in + -20in + -1inx = 0 + -20in Combine like terms: 20in + -20in = 0 -20co + cox + 0 + -1inx = 0 + -20in -20co + cox + -1inx = 0 + -20in Remove the zero: -20co + cox + -1inx = -20in Add 'inx' to each side of the equation. -20co + cox + -1inx + inx = -20in + inx Combine like terms: -1inx + inx = 0 -20co + cox + 0 = -20in + inx -20co + cox = -20in + inx 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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