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Simplifying cot(5x + 2) = tan(2x + 8) Reorder the terms: cot(2 + 5x) = tan(2x + 8) (2 * cot + 5x * cot) = tan(2x + 8) (2cot + 5cotx) = tan(2x + 8) Reorder the terms: 2cot + 5cotx = ant(8 + 2x) 2cot + 5cotx = (8 * ant + 2x * ant) 2cot + 5cotx = (8ant + 2antx) Solving 2cot + 5cotx = 8ant + 2antx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Reorder the terms: -8ant + -2antx + 2cot + 5cotx = 8ant + 2antx + -8ant + -2antx Reorder the terms: -8ant + -2antx + 2cot + 5cotx = 8ant + -8ant + 2antx + -2antx Combine like terms: 8ant + -8ant = 0 -8ant + -2antx + 2cot + 5cotx = 0 + 2antx + -2antx -8ant + -2antx + 2cot + 5cotx = 2antx + -2antx Combine like terms: 2antx + -2antx = 0 -8ant + -2antx + 2cot + 5cotx = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-8an + -2anx + 2co + 5cox) = 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 '(-8an + -2anx + 2co + 5cox)' equal to zero and attempt to solve: Simplifying -8an + -2anx + 2co + 5cox = 0 Solving -8an + -2anx + 2co + 5cox = 0 Move all terms containing c to the left, all other terms to the right. Add '8an' to each side of the equation. -8an + -2anx + 2co + 8an + 5cox = 0 + 8an Reorder the terms: -8an + 8an + -2anx + 2co + 5cox = 0 + 8an Combine like terms: -8an + 8an = 0 0 + -2anx + 2co + 5cox = 0 + 8an -2anx + 2co + 5cox = 0 + 8an Remove the zero: -2anx + 2co + 5cox = 8an Add '2anx' to each side of the equation. -2anx + 2co + 2anx + 5cox = 8an + 2anx Reorder the terms: -2anx + 2anx + 2co + 5cox = 8an + 2anx Combine like terms: -2anx + 2anx = 0 0 + 2co + 5cox = 8an + 2anx 2co + 5cox = 8an + 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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