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Simplifying tan(2x + -30) = cot(x + 27) Reorder the terms: ant(-30 + 2x) = cot(x + 27) (-30 * ant + 2x * ant) = cot(x + 27) (-30ant + 2antx) = cot(x + 27) Reorder the terms: -30ant + 2antx = cot(27 + x) -30ant + 2antx = (27 * cot + x * cot) -30ant + 2antx = (27cot + cotx) Solving -30ant + 2antx = 27cot + cotx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Reorder the terms: -30ant + 2antx + -27cot + -1cotx = 27cot + -27cot + cotx + -1cotx Combine like terms: 27cot + -27cot = 0 -30ant + 2antx + -27cot + -1cotx = 0 + cotx + -1cotx -30ant + 2antx + -27cot + -1cotx = cotx + -1cotx Combine like terms: cotx + -1cotx = 0 -30ant + 2antx + -27cot + -1cotx = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-30an + 2anx + -27co + -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 '(-30an + 2anx + -27co + -1cox)' equal to zero and attempt to solve: Simplifying -30an + 2anx + -27co + -1cox = 0 Solving -30an + 2anx + -27co + -1cox = 0 Move all terms containing a to the left, all other terms to the right. Add '27co' to each side of the equation. -30an + 2anx + -27co + 27co + -1cox = 0 + 27co Combine like terms: -27co + 27co = 0 -30an + 2anx + 0 + -1cox = 0 + 27co -30an + 2anx + -1cox = 0 + 27co Remove the zero: -30an + 2anx + -1cox = 27co Add 'cox' to each side of the equation. -30an + 2anx + -1cox + cox = 27co + cox Combine like terms: -1cox + cox = 0 -30an + 2anx + 0 = 27co + cox -30an + 2anx = 27co + 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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