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Simplifying cot(14 + x) = tan(2x + 10) (14 * cot + x * cot) = tan(2x + 10) (14cot + cotx) = tan(2x + 10) Reorder the terms: 14cot + cotx = ant(10 + 2x) 14cot + cotx = (10 * ant + 2x * ant) 14cot + cotx = (10ant + 2antx) Solving 14cot + cotx = 10ant + 2antx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Reorder the terms: -10ant + -2antx + 14cot + cotx = 10ant + 2antx + -10ant + -2antx Reorder the terms: -10ant + -2antx + 14cot + cotx = 10ant + -10ant + 2antx + -2antx Combine like terms: 10ant + -10ant = 0 -10ant + -2antx + 14cot + cotx = 0 + 2antx + -2antx -10ant + -2antx + 14cot + cotx = 2antx + -2antx Combine like terms: 2antx + -2antx = 0 -10ant + -2antx + 14cot + cotx = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-10an + -2anx + 14co + cox) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing c 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 '(-10an + -2anx + 14co + cox)' equal to zero and attempt to solve: Simplifying -10an + -2anx + 14co + cox = 0 Solving -10an + -2anx + 14co + cox = 0 Move all terms containing c to the left, all other terms to the right. Add '10an' to each side of the equation. -10an + -2anx + 14co + 10an + cox = 0 + 10an Reorder the terms: -10an + 10an + -2anx + 14co + cox = 0 + 10an Combine like terms: -10an + 10an = 0 0 + -2anx + 14co + cox = 0 + 10an -2anx + 14co + cox = 0 + 10an Remove the zero: -2anx + 14co + cox = 10an Add '2anx' to each side of the equation. -2anx + 14co + 2anx + cox = 10an + 2anx Reorder the terms: -2anx + 2anx + 14co + cox = 10an + 2anx Combine like terms: -2anx + 2anx = 0 0 + 14co + cox = 10an + 2anx 14co + cox = 10an + 2anx 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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