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Simplifying 3cos(x + 10) = 3sin(x + 100) Reorder the terms: 3cos(10 + x) = 3sin(x + 100) (10 * 3cos + x * 3cos) = 3sin(x + 100) (30cos + 3cosx) = 3sin(x + 100) Reorder the terms: 30cos + 3cosx = 3ins(100 + x) 30cos + 3cosx = (100 * 3ins + x * 3ins) 30cos + 3cosx = (300ins + 3insx) Solving 30cos + 3cosx = 300ins + 3insx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Reorder the terms: 30cos + 3cosx + -300ins + -3insx = 300ins + -300ins + 3insx + -3insx Combine like terms: 300ins + -300ins = 0 30cos + 3cosx + -300ins + -3insx = 0 + 3insx + -3insx 30cos + 3cosx + -300ins + -3insx = 3insx + -3insx Combine like terms: 3insx + -3insx = 0 30cos + 3cosx + -300ins + -3insx = 0 Factor out the Greatest Common Factor (GCF), '3s'. 3s(10co + cox + -100in + -1inx) = 0 Ignore the factor 3.Subproblem 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 '(10co + cox + -100in + -1inx)' equal to zero and attempt to solve: Simplifying 10co + cox + -100in + -1inx = 0 Solving 10co + cox + -100in + -1inx = 0 Move all terms containing c to the left, all other terms to the right. Add '100in' to each side of the equation. 10co + cox + -100in + 100in + -1inx = 0 + 100in Combine like terms: -100in + 100in = 0 10co + cox + 0 + -1inx = 0 + 100in 10co + cox + -1inx = 0 + 100in Remove the zero: 10co + cox + -1inx = 100in Add 'inx' to each side of the equation. 10co + cox + -1inx + inx = 100in + inx Combine like terms: -1inx + inx = 0 10co + cox + 0 = 100in + inx 10co + cox = 100in + inx 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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