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Simplifying tan(3x + -7) = cot(5x + 15) Reorder the terms: ant(-7 + 3x) = cot(5x + 15) (-7 * ant + 3x * ant) = cot(5x + 15) (-7ant + 3antx) = cot(5x + 15) Reorder the terms: -7ant + 3antx = cot(15 + 5x) -7ant + 3antx = (15 * cot + 5x * cot) -7ant + 3antx = (15cot + 5cotx) Solving -7ant + 3antx = 15cot + 5cotx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Reorder the terms: -7ant + 3antx + -15cot + -5cotx = 15cot + -15cot + 5cotx + -5cotx Combine like terms: 15cot + -15cot = 0 -7ant + 3antx + -15cot + -5cotx = 0 + 5cotx + -5cotx -7ant + 3antx + -15cot + -5cotx = 5cotx + -5cotx Combine like terms: 5cotx + -5cotx = 0 -7ant + 3antx + -15cot + -5cotx = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-7an + 3anx + -15co + -5cox) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing a to the left, all other terms to the right. Add '-1t' to each side of the equation. t + -1t = 0 + -1t Remove the zero: 0 = -1t Simplifying 0 = -1t 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 '(-7an + 3anx + -15co + -5cox)' equal to zero and attempt to solve: Simplifying -7an + 3anx + -15co + -5cox = 0 Solving -7an + 3anx + -15co + -5cox = 0 Move all terms containing a to the left, all other terms to the right. Add '15co' to each side of the equation. -7an + 3anx + -15co + 15co + -5cox = 0 + 15co Combine like terms: -15co + 15co = 0 -7an + 3anx + 0 + -5cox = 0 + 15co -7an + 3anx + -5cox = 0 + 15co Remove the zero: -7an + 3anx + -5cox = 15co Add '5cox' to each side of the equation. -7an + 3anx + -5cox + 5cox = 15co + 5cox Combine like terms: -5cox + 5cox = 0 -7an + 3anx + 0 = 15co + 5cox -7an + 3anx = 15co + 5cox 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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