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Simplifying sin(2x + 30) = cos(3x + 5) Reorder the terms: ins(30 + 2x) = cos(3x + 5) (30 * ins + 2x * ins) = cos(3x + 5) (30ins + 2insx) = cos(3x + 5) Reorder the terms: 30ins + 2insx = cos(5 + 3x) 30ins + 2insx = (5 * cos + 3x * cos) 30ins + 2insx = (5cos + 3cosx) Solving 30ins + 2insx = 5cos + 3cosx Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Reorder the terms: -5cos + -3cosx + 30ins + 2insx = 5cos + 3cosx + -5cos + -3cosx Reorder the terms: -5cos + -3cosx + 30ins + 2insx = 5cos + -5cos + 3cosx + -3cosx Combine like terms: 5cos + -5cos = 0 -5cos + -3cosx + 30ins + 2insx = 0 + 3cosx + -3cosx -5cos + -3cosx + 30ins + 2insx = 3cosx + -3cosx Combine like terms: 3cosx + -3cosx = 0 -5cos + -3cosx + 30ins + 2insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(-5co + -3cox + 30in + 2inx) = 0Subproblem 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 + -3cox + 30in + 2inx)' equal to zero and attempt to solve: Simplifying -5co + -3cox + 30in + 2inx = 0 Solving -5co + -3cox + 30in + 2inx = 0 Move all terms containing i to the left, all other terms to the right. Add '5co' to each side of the equation. -5co + -3cox + 30in + 5co + 2inx = 0 + 5co Reorder the terms: -5co + 5co + -3cox + 30in + 2inx = 0 + 5co Combine like terms: -5co + 5co = 0 0 + -3cox + 30in + 2inx = 0 + 5co -3cox + 30in + 2inx = 0 + 5co Remove the zero: -3cox + 30in + 2inx = 5co Add '3cox' to each side of the equation. -3cox + 30in + 3cox + 2inx = 5co + 3cox Reorder the terms: -3cox + 3cox + 30in + 2inx = 5co + 3cox Combine like terms: -3cox + 3cox = 0 0 + 30in + 2inx = 5co + 3cox 30in + 2inx = 5co + 3cox 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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