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Simplifying 3cos(x + 40) + 4sin(x + 20) = 0 Reorder the terms: 3cos(40 + x) + 4sin(x + 20) = 0 (40 * 3cos + x * 3cos) + 4sin(x + 20) = 0 (120cos + 3cosx) + 4sin(x + 20) = 0 Reorder the terms: 120cos + 3cosx + 4ins(20 + x) = 0 120cos + 3cosx + (20 * 4ins + x * 4ins) = 0 120cos + 3cosx + (80ins + 4insx) = 0 Solving 120cos + 3cosx + 80ins + 4insx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-80ins' to each side of the equation. 120cos + 3cosx + 80ins + -80ins + 4insx = 0 + -80ins Combine like terms: 80ins + -80ins = 0 120cos + 3cosx + 0 + 4insx = 0 + -80ins 120cos + 3cosx + 4insx = 0 + -80ins Remove the zero: 120cos + 3cosx + 4insx = -80ins Add '-4insx' to each side of the equation. 120cos + 3cosx + 4insx + -4insx = -80ins + -4insx Combine like terms: 4insx + -4insx = 0 120cos + 3cosx + 0 = -80ins + -4insx 120cos + 3cosx = -80ins + -4insx Reorder the terms: 120cos + 3cosx + 80ins + 4insx = -80ins + 80ins + -4insx + 4insx Combine like terms: -80ins + 80ins = 0 120cos + 3cosx + 80ins + 4insx = 0 + -4insx + 4insx 120cos + 3cosx + 80ins + 4insx = -4insx + 4insx Combine like terms: -4insx + 4insx = 0 120cos + 3cosx + 80ins + 4insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(120co + 3cox + 80in + 4inx) = 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 '(120co + 3cox + 80in + 4inx)' equal to zero and attempt to solve: Simplifying 120co + 3cox + 80in + 4inx = 0 Solving 120co + 3cox + 80in + 4inx = 0 Move all terms containing c to the left, all other terms to the right. Add '-80in' to each side of the equation. 120co + 3cox + 80in + -80in + 4inx = 0 + -80in Combine like terms: 80in + -80in = 0 120co + 3cox + 0 + 4inx = 0 + -80in 120co + 3cox + 4inx = 0 + -80in Remove the zero: 120co + 3cox + 4inx = -80in Add '-4inx' to each side of the equation. 120co + 3cox + 4inx + -4inx = -80in + -4inx Combine like terms: 4inx + -4inx = 0 120co + 3cox + 0 = -80in + -4inx 120co + 3cox = -80in + -4inx 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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