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Simplifying tan(30 + -2x) = cot(4x + 30) (30 * ant + -2x * ant) = cot(4x + 30) (30ant + -2antx) = cot(4x + 30) Reorder the terms: 30ant + -2antx = cot(30 + 4x) 30ant + -2antx = (30 * cot + 4x * cot) 30ant + -2antx = (30cot + 4cotx) Solving 30ant + -2antx = 30cot + 4cotx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Reorder the terms: 30ant + -2antx + -30cot + -4cotx = 30cot + -30cot + 4cotx + -4cotx Combine like terms: 30cot + -30cot = 0 30ant + -2antx + -30cot + -4cotx = 0 + 4cotx + -4cotx 30ant + -2antx + -30cot + -4cotx = 4cotx + -4cotx Combine like terms: 4cotx + -4cotx = 0 30ant + -2antx + -30cot + -4cotx = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(15an + -1anx + -15co + -2cox) = 0 Ignore the factor 2.Subproblem 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 '(15an + -1anx + -15co + -2cox)' equal to zero and attempt to solve: Simplifying 15an + -1anx + -15co + -2cox = 0 Solving 15an + -1anx + -15co + -2cox = 0 Move all terms containing a to the left, all other terms to the right. Add '15co' to each side of the equation. 15an + -1anx + -15co + 15co + -2cox = 0 + 15co Combine like terms: -15co + 15co = 0 15an + -1anx + 0 + -2cox = 0 + 15co 15an + -1anx + -2cox = 0 + 15co Remove the zero: 15an + -1anx + -2cox = 15co Add '2cox' to each side of the equation. 15an + -1anx + -2cox + 2cox = 15co + 2cox Combine like terms: -2cox + 2cox = 0 15an + -1anx + 0 = 15co + 2cox 15an + -1anx = 15co + 2cox 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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