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Simplifying tan(5x + 8) = cot(12x + 14) Reorder the terms: ant(8 + 5x) = cot(12x + 14) (8 * ant + 5x * ant) = cot(12x + 14) (8ant + 5antx) = cot(12x + 14) Reorder the terms: 8ant + 5antx = cot(14 + 12x) 8ant + 5antx = (14 * cot + 12x * cot) 8ant + 5antx = (14cot + 12cotx) Solving 8ant + 5antx = 14cot + 12cotx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Reorder the terms: 8ant + 5antx + -14cot + -12cotx = 14cot + -14cot + 12cotx + -12cotx Combine like terms: 14cot + -14cot = 0 8ant + 5antx + -14cot + -12cotx = 0 + 12cotx + -12cotx 8ant + 5antx + -14cot + -12cotx = 12cotx + -12cotx Combine like terms: 12cotx + -12cotx = 0 8ant + 5antx + -14cot + -12cotx = 0 Factor out the Greatest Common Factor (GCF), 't'. t(8an + 5anx + -14co + -12cox) = 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 '(8an + 5anx + -14co + -12cox)' equal to zero and attempt to solve: Simplifying 8an + 5anx + -14co + -12cox = 0 Solving 8an + 5anx + -14co + -12cox = 0 Move all terms containing a to the left, all other terms to the right. Add '14co' to each side of the equation. 8an + 5anx + -14co + 14co + -12cox = 0 + 14co Combine like terms: -14co + 14co = 0 8an + 5anx + 0 + -12cox = 0 + 14co 8an + 5anx + -12cox = 0 + 14co Remove the zero: 8an + 5anx + -12cox = 14co Add '12cox' to each side of the equation. 8an + 5anx + -12cox + 12cox = 14co + 12cox Combine like terms: -12cox + 12cox = 0 8an + 5anx + 0 = 14co + 12cox 8an + 5anx = 14co + 12cox 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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