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