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Simplifying Sen(2x + 80) = cos(4x + 20) Reorder the terms: enS(80 + 2x) = cos(4x + 20) (80 * enS + 2x * enS) = cos(4x + 20) (80enS + 2enxS) = cos(4x + 20) Reorder the terms: 80enS + 2enxS = cos(20 + 4x) 80enS + 2enxS = (20 * cos + 4x * cos) 80enS + 2enxS = (20cos + 4cosx) Solving 80enS + 2enxS = 20cos + 4cosx Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Reorder the terms: -20cos + -4cosx + 80enS + 2enxS = 20cos + 4cosx + -20cos + -4cosx Reorder the terms: -20cos + -4cosx + 80enS + 2enxS = 20cos + -20cos + 4cosx + -4cosx Combine like terms: 20cos + -20cos = 0 -20cos + -4cosx + 80enS + 2enxS = 0 + 4cosx + -4cosx -20cos + -4cosx + 80enS + 2enxS = 4cosx + -4cosx Combine like terms: 4cosx + -4cosx = 0 -20cos + -4cosx + 80enS + 2enxS = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10cos + -2cosx + 40enS + enxS) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10cos + -2cosx + 40enS + enxS)' equal to zero and attempt to solve: Simplifying -10cos + -2cosx + 40enS + enxS = 0 Solving -10cos + -2cosx + 40enS + enxS = 0 Move all terms containing e to the left, all other terms to the right. Add '10cos' to each side of the equation. -10cos + -2cosx + 40enS + 10cos + enxS = 0 + 10cos Reorder the terms: -10cos + 10cos + -2cosx + 40enS + enxS = 0 + 10cos Combine like terms: -10cos + 10cos = 0 0 + -2cosx + 40enS + enxS = 0 + 10cos -2cosx + 40enS + enxS = 0 + 10cos Remove the zero: -2cosx + 40enS + enxS = 10cos Add '2cosx' to each side of the equation. -2cosx + 40enS + 2cosx + enxS = 10cos + 2cosx Reorder the terms: -2cosx + 2cosx + 40enS + enxS = 10cos + 2cosx Combine like terms: -2cosx + 2cosx = 0 0 + 40enS + enxS = 10cos + 2cosx 40enS + enxS = 10cos + 2cosx 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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