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Simplifying cos(2x + 30) = sin(3x + -60) Reorder the terms: cos(30 + 2x) = sin(3x + -60) (30 * cos + 2x * cos) = sin(3x + -60) (30cos + 2cosx) = sin(3x + -60) Reorder the terms: 30cos + 2cosx = ins(-60 + 3x) 30cos + 2cosx = (-60 * ins + 3x * ins) 30cos + 2cosx = (-60ins + 3insx) Solving 30cos + 2cosx = -60ins + 3insx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Reorder the terms: 30cos + 2cosx + 60ins + -3insx = -60ins + 60ins + 3insx + -3insx Combine like terms: -60ins + 60ins = 0 30cos + 2cosx + 60ins + -3insx = 0 + 3insx + -3insx 30cos + 2cosx + 60ins + -3insx = 3insx + -3insx Combine like terms: 3insx + -3insx = 0 30cos + 2cosx + 60ins + -3insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(30co + 2cox + 60in + -3inx) = 0Subproblem 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 '(30co + 2cox + 60in + -3inx)' equal to zero and attempt to solve: Simplifying 30co + 2cox + 60in + -3inx = 0 Solving 30co + 2cox + 60in + -3inx = 0 Move all terms containing c to the left, all other terms to the right. Add '-60in' to each side of the equation. 30co + 2cox + 60in + -60in + -3inx = 0 + -60in Combine like terms: 60in + -60in = 0 30co + 2cox + 0 + -3inx = 0 + -60in 30co + 2cox + -3inx = 0 + -60in Remove the zero: 30co + 2cox + -3inx = -60in Add '3inx' to each side of the equation. 30co + 2cox + -3inx + 3inx = -60in + 3inx Combine like terms: -3inx + 3inx = 0 30co + 2cox + 0 = -60in + 3inx 30co + 2cox = -60in + 3inx 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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