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Simplifying 2cos(x + 30) = sin(x + -30) Reorder the terms: 2cos(30 + x) = sin(x + -30) (30 * 2cos + x * 2cos) = sin(x + -30) (60cos + 2cosx) = sin(x + -30) Reorder the terms: 60cos + 2cosx = ins(-30 + x) 60cos + 2cosx = (-30 * ins + x * ins) 60cos + 2cosx = (-30ins + insx) Solving 60cos + 2cosx = -30ins + insx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Reorder the terms: 60cos + 2cosx + 30ins + -1insx = -30ins + 30ins + insx + -1insx Combine like terms: -30ins + 30ins = 0 60cos + 2cosx + 30ins + -1insx = 0 + insx + -1insx 60cos + 2cosx + 30ins + -1insx = insx + -1insx Combine like terms: insx + -1insx = 0 60cos + 2cosx + 30ins + -1insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(60co + 2cox + 30in + -1inx) = 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 '(60co + 2cox + 30in + -1inx)' equal to zero and attempt to solve: Simplifying 60co + 2cox + 30in + -1inx = 0 Solving 60co + 2cox + 30in + -1inx = 0 Move all terms containing c to the left, all other terms to the right. Add '-30in' to each side of the equation. 60co + 2cox + 30in + -30in + -1inx = 0 + -30in Combine like terms: 30in + -30in = 0 60co + 2cox + 0 + -1inx = 0 + -30in 60co + 2cox + -1inx = 0 + -30in Remove the zero: 60co + 2cox + -1inx = -30in Add 'inx' to each side of the equation. 60co + 2cox + -1inx + inx = -30in + inx Combine like terms: -1inx + inx = 0 60co + 2cox + 0 = -30in + inx 60co + 2cox = -30in + 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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