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Simplifying cot(2x + -30) = tan(3x + 10) Reorder the terms: cot(-30 + 2x) = tan(3x + 10) (-30 * cot + 2x * cot) = tan(3x + 10) (-30cot + 2cotx) = tan(3x + 10) Reorder the terms: -30cot + 2cotx = ant(10 + 3x) -30cot + 2cotx = (10 * ant + 3x * ant) -30cot + 2cotx = (10ant + 3antx) Solving -30cot + 2cotx = 10ant + 3antx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Reorder the terms: -10ant + -3antx + -30cot + 2cotx = 10ant + 3antx + -10ant + -3antx Reorder the terms: -10ant + -3antx + -30cot + 2cotx = 10ant + -10ant + 3antx + -3antx Combine like terms: 10ant + -10ant = 0 -10ant + -3antx + -30cot + 2cotx = 0 + 3antx + -3antx -10ant + -3antx + -30cot + 2cotx = 3antx + -3antx Combine like terms: 3antx + -3antx = 0 -10ant + -3antx + -30cot + 2cotx = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-10an + -3anx + -30co + 2cox) = 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 + -3anx + -30co + 2cox)' equal to zero and attempt to solve: Simplifying -10an + -3anx + -30co + 2cox = 0 Solving -10an + -3anx + -30co + 2cox = 0 Move all terms containing c to the left, all other terms to the right. Add '10an' to each side of the equation. -10an + -3anx + -30co + 10an + 2cox = 0 + 10an Reorder the terms: -10an + 10an + -3anx + -30co + 2cox = 0 + 10an Combine like terms: -10an + 10an = 0 0 + -3anx + -30co + 2cox = 0 + 10an -3anx + -30co + 2cox = 0 + 10an Remove the zero: -3anx + -30co + 2cox = 10an Add '3anx' to each side of the equation. -3anx + -30co + 3anx + 2cox = 10an + 3anx Reorder the terms: -3anx + 3anx + -30co + 2cox = 10an + 3anx Combine like terms: -3anx + 3anx = 0 0 + -30co + 2cox = 10an + 3anx -30co + 2cox = 10an + 3anx 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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