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Simplifying 5sinx + 7cosx = 3ctgx Reorder the terms: 7cosx + 5insx = 3ctgx Solving 7cosx + 5insx = 3cgtx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3cgtx' to each side of the equation. 7cosx + -3cgtx + 5insx = 3cgtx + -3cgtx Reorder the terms: -3cgtx + 7cosx + 5insx = 3cgtx + -3cgtx Combine like terms: 3cgtx + -3cgtx = 0 -3cgtx + 7cosx + 5insx = 0 Add '-5insx' to each side of the equation. -3cgtx + 7cosx + 5insx + -5insx = 0 + -5insx Combine like terms: 5insx + -5insx = 0 -3cgtx + 7cosx + 0 = 0 + -5insx -3cgtx + 7cosx = 0 + -5insx Remove the zero: -3cgtx + 7cosx = -5insx Combine like terms: -5insx + 5insx = 0 -3cgtx + 7cosx + 5insx = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-3cgt + 7cos + 5ins) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing c to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(-3cgt + 7cos + 5ins)' equal to zero and attempt to solve: Simplifying -3cgt + 7cos + 5ins = 0 Solving -3cgt + 7cos + 5ins = 0 Move all terms containing c to the left, all other terms to the right. Add '-5ins' to each side of the equation. -3cgt + 7cos + 5ins + -5ins = 0 + -5ins Combine like terms: 5ins + -5ins = 0 -3cgt + 7cos + 0 = 0 + -5ins -3cgt + 7cos = 0 + -5ins Remove the zero: -3cgt + 7cos = -5ins 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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