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Simplifying sin(x + 30) = 2cos(x + 45) Reorder the terms: ins(30 + x) = 2cos(x + 45) (30 * ins + x * ins) = 2cos(x + 45) (30ins + insx) = 2cos(x + 45) Reorder the terms: 30ins + insx = 2cos(45 + x) 30ins + insx = (45 * 2cos + x * 2cos) 30ins + insx = (90cos + 2cosx) Solving 30ins + insx = 90cos + 2cosx Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Reorder the terms: -90cos + -2cosx + 30ins + insx = 90cos + 2cosx + -90cos + -2cosx Reorder the terms: -90cos + -2cosx + 30ins + insx = 90cos + -90cos + 2cosx + -2cosx Combine like terms: 90cos + -90cos = 0 -90cos + -2cosx + 30ins + insx = 0 + 2cosx + -2cosx -90cos + -2cosx + 30ins + insx = 2cosx + -2cosx Combine like terms: 2cosx + -2cosx = 0 -90cos + -2cosx + 30ins + insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(-90co + -2cox + 30in + inx) = 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 '(-90co + -2cox + 30in + inx)' equal to zero and attempt to solve: Simplifying -90co + -2cox + 30in + inx = 0 Solving -90co + -2cox + 30in + inx = 0 Move all terms containing i to the left, all other terms to the right. Add '90co' to each side of the equation. -90co + -2cox + 30in + 90co + inx = 0 + 90co Reorder the terms: -90co + 90co + -2cox + 30in + inx = 0 + 90co Combine like terms: -90co + 90co = 0 0 + -2cox + 30in + inx = 0 + 90co -2cox + 30in + inx = 0 + 90co Remove the zero: -2cox + 30in + inx = 90co Add '2cox' to each side of the equation. -2cox + 30in + 2cox + inx = 90co + 2cox Reorder the terms: -2cox + 2cox + 30in + inx = 90co + 2cox Combine like terms: -2cox + 2cox = 0 0 + 30in + inx = 90co + 2cox 30in + inx = 90co + 2cox 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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