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Simplifying 2sin(x + 40) = 3cos(x + -10) Reorder the terms: 2ins(40 + x) = 3cos(x + -10) (40 * 2ins + x * 2ins) = 3cos(x + -10) (80ins + 2insx) = 3cos(x + -10) Reorder the terms: 80ins + 2insx = 3cos(-10 + x) 80ins + 2insx = (-10 * 3cos + x * 3cos) 80ins + 2insx = (-30cos + 3cosx) Solving 80ins + 2insx = -30cos + 3cosx Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Reorder the terms: 30cos + -3cosx + 80ins + 2insx = -30cos + 3cosx + 30cos + -3cosx Reorder the terms: 30cos + -3cosx + 80ins + 2insx = -30cos + 30cos + 3cosx + -3cosx Combine like terms: -30cos + 30cos = 0 30cos + -3cosx + 80ins + 2insx = 0 + 3cosx + -3cosx 30cos + -3cosx + 80ins + 2insx = 3cosx + -3cosx Combine like terms: 3cosx + -3cosx = 0 30cos + -3cosx + 80ins + 2insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(30co + -3cox + 80in + 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 '(30co + -3cox + 80in + 2inx)' equal to zero and attempt to solve: Simplifying 30co + -3cox + 80in + 2inx = 0 Solving 30co + -3cox + 80in + 2inx = 0 Move all terms containing i to the left, all other terms to the right. Add '-30co' to each side of the equation. 30co + -3cox + 80in + -30co + 2inx = 0 + -30co Reorder the terms: 30co + -30co + -3cox + 80in + 2inx = 0 + -30co Combine like terms: 30co + -30co = 0 0 + -3cox + 80in + 2inx = 0 + -30co -3cox + 80in + 2inx = 0 + -30co Remove the zero: -3cox + 80in + 2inx = -30co Add '3cox' to each side of the equation. -3cox + 80in + 3cox + 2inx = -30co + 3cox Reorder the terms: -3cox + 3cox + 80in + 2inx = -30co + 3cox Combine like terms: -3cox + 3cox = 0 0 + 80in + 2inx = -30co + 3cox 80in + 2inx = -30co + 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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