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Simplifying tanx + tan(x + 120) + tan(x + 240) = 2tan(2x) Reorder the terms: antx + ant(120 + x) + tan(x + 240) = 2tan(2x) antx + (120 * ant + x * ant) + tan(x + 240) = 2tan(2x) antx + (120ant + antx) + tan(x + 240) = 2tan(2x) Reorder the terms: antx + 120ant + antx + ant(240 + x) = 2tan(2x) antx + 120ant + antx + (240 * ant + x * ant) = 2tan(2x) antx + 120ant + antx + (240ant + antx) = 2tan(2x) Reorder the terms: 120ant + 240ant + antx + antx + antx = 2tan(2x) Combine like terms: 120ant + 240ant = 360ant 360ant + antx + antx + antx = 2tan(2x) Combine like terms: antx + antx = 2antx 360ant + 2antx + antx = 2tan(2x) Combine like terms: 2antx + antx = 3antx 360ant + 3antx = 2tan(2x) Remove parenthesis around (2x) 360ant + 3antx = 2ant * 2x Reorder the terms for easier multiplication: 360ant + 3antx = 2 * 2ant * x Multiply 2 * 2 360ant + 3antx = 4ant * x Multiply ant * x 360ant + 3antx = 4antx Solving 360ant + 3antx = 4antx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4antx' to each side of the equation. 360ant + 3antx + -4antx = 4antx + -4antx Combine like terms: 3antx + -4antx = -1antx 360ant + -1antx = 4antx + -4antx Combine like terms: 4antx + -4antx = 0 360ant + -1antx = 0 Factor out the Greatest Common Factor (GCF), 'ant'. ant(360 + -1x) = 0Subproblem 1
Set the factor 'ant' equal to zero and attempt to solve: Simplifying ant = 0 Solving ant = 0 Move all terms containing a to the left, all other terms to the right. Simplifying ant = 0 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 '(360 + -1x)' equal to zero and attempt to solve: Simplifying 360 + -1x = 0 Solving 360 + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add '-360' to each side of the equation. 360 + -360 + -1x = 0 + -360 Combine like terms: 360 + -360 = 0 0 + -1x = 0 + -360 -1x = 0 + -360 Combine like terms: 0 + -360 = -360 -1x = -360 Add 'x' to each side of the equation. -1x + x = -360 + x Combine like terms: -1x + x = 0 0 = -360 + x Simplifying 0 = -360 + x 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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