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Simplifying cos(x + -45) + -3sin(x + 30) = 0 Reorder the terms: cos(-45 + x) + -3sin(x + 30) = 0 (-45 * cos + x * cos) + -3sin(x + 30) = 0 (-45cos + cosx) + -3sin(x + 30) = 0 Reorder the terms: -45cos + cosx + -3ins(30 + x) = 0 -45cos + cosx + (30 * -3ins + x * -3ins) = 0 -45cos + cosx + (-90ins + -3insx) = 0 Solving -45cos + cosx + -90ins + -3insx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '90ins' to each side of the equation. -45cos + cosx + -90ins + 90ins + -3insx = 0 + 90ins Combine like terms: -90ins + 90ins = 0 -45cos + cosx + 0 + -3insx = 0 + 90ins -45cos + cosx + -3insx = 0 + 90ins Remove the zero: -45cos + cosx + -3insx = 90ins Add '3insx' to each side of the equation. -45cos + cosx + -3insx + 3insx = 90ins + 3insx Combine like terms: -3insx + 3insx = 0 -45cos + cosx + 0 = 90ins + 3insx -45cos + cosx = 90ins + 3insx Reorder the terms: -45cos + cosx + -90ins + -3insx = 90ins + -90ins + 3insx + -3insx Combine like terms: 90ins + -90ins = 0 -45cos + cosx + -90ins + -3insx = 0 + 3insx + -3insx -45cos + cosx + -90ins + -3insx = 3insx + -3insx Combine like terms: 3insx + -3insx = 0 -45cos + cosx + -90ins + -3insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(-45co + cox + -90in + -3inx) = 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 '(-45co + cox + -90in + -3inx)' equal to zero and attempt to solve: Simplifying -45co + cox + -90in + -3inx = 0 Solving -45co + cox + -90in + -3inx = 0 Move all terms containing c to the left, all other terms to the right. Add '90in' to each side of the equation. -45co + cox + -90in + 90in + -3inx = 0 + 90in Combine like terms: -90in + 90in = 0 -45co + cox + 0 + -3inx = 0 + 90in -45co + cox + -3inx = 0 + 90in Remove the zero: -45co + cox + -3inx = 90in Add '3inx' to each side of the equation. -45co + cox + -3inx + 3inx = 90in + 3inx Combine like terms: -3inx + 3inx = 0 -45co + cox + 0 = 90in + 3inx -45co + cox = 90in + 3inx 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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