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Simplifying sin(2x + 30) = cos(8x + -40) Reorder the terms: ins(30 + 2x) = cos(8x + -40) (30 * ins + 2x * ins) = cos(8x + -40) (30ins + 2insx) = cos(8x + -40) Reorder the terms: 30ins + 2insx = cos(-40 + 8x) 30ins + 2insx = (-40 * cos + 8x * cos) 30ins + 2insx = (-40cos + 8cosx) Solving 30ins + 2insx = -40cos + 8cosx Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Reorder the terms: 40cos + -8cosx + 30ins + 2insx = -40cos + 8cosx + 40cos + -8cosx Reorder the terms: 40cos + -8cosx + 30ins + 2insx = -40cos + 40cos + 8cosx + -8cosx Combine like terms: -40cos + 40cos = 0 40cos + -8cosx + 30ins + 2insx = 0 + 8cosx + -8cosx 40cos + -8cosx + 30ins + 2insx = 8cosx + -8cosx Combine like terms: 8cosx + -8cosx = 0 40cos + -8cosx + 30ins + 2insx = 0 Factor out the Greatest Common Factor (GCF), '2s'. 2s(20co + -4cox + 15in + inx) = 0 Ignore the factor 2.Subproblem 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 '(20co + -4cox + 15in + inx)' equal to zero and attempt to solve: Simplifying 20co + -4cox + 15in + inx = 0 Solving 20co + -4cox + 15in + inx = 0 Move all terms containing i to the left, all other terms to the right. Add '-20co' to each side of the equation. 20co + -4cox + 15in + -20co + inx = 0 + -20co Reorder the terms: 20co + -20co + -4cox + 15in + inx = 0 + -20co Combine like terms: 20co + -20co = 0 0 + -4cox + 15in + inx = 0 + -20co -4cox + 15in + inx = 0 + -20co Remove the zero: -4cox + 15in + inx = -20co Add '4cox' to each side of the equation. -4cox + 15in + 4cox + inx = -20co + 4cox Reorder the terms: -4cox + 4cox + 15in + inx = -20co + 4cox Combine like terms: -4cox + 4cox = 0 0 + 15in + inx = -20co + 4cox 15in + inx = -20co + 4cox 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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