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Simplifying tan(2x + 12) = cot(x + -21) Reorder the terms: ant(12 + 2x) = cot(x + -21) (12 * ant + 2x * ant) = cot(x + -21) (12ant + 2antx) = cot(x + -21) Reorder the terms: 12ant + 2antx = cot(-21 + x) 12ant + 2antx = (-21 * cot + x * cot) 12ant + 2antx = (-21cot + cotx) Solving 12ant + 2antx = -21cot + cotx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Reorder the terms: 12ant + 2antx + 21cot + -1cotx = -21cot + 21cot + cotx + -1cotx Combine like terms: -21cot + 21cot = 0 12ant + 2antx + 21cot + -1cotx = 0 + cotx + -1cotx 12ant + 2antx + 21cot + -1cotx = cotx + -1cotx Combine like terms: cotx + -1cotx = 0 12ant + 2antx + 21cot + -1cotx = 0 Factor out the Greatest Common Factor (GCF), 't'. t(12an + 2anx + 21co + -1cox) = 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 '(12an + 2anx + 21co + -1cox)' equal to zero and attempt to solve: Simplifying 12an + 2anx + 21co + -1cox = 0 Solving 12an + 2anx + 21co + -1cox = 0 Move all terms containing a to the left, all other terms to the right. Add '-21co' to each side of the equation. 12an + 2anx + 21co + -21co + -1cox = 0 + -21co Combine like terms: 21co + -21co = 0 12an + 2anx + 0 + -1cox = 0 + -21co 12an + 2anx + -1cox = 0 + -21co Remove the zero: 12an + 2anx + -1cox = -21co Add 'cox' to each side of the equation. 12an + 2anx + -1cox + cox = -21co + cox Combine like terms: -1cox + cox = 0 12an + 2anx + 0 = -21co + cox 12an + 2anx = -21co + cox 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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