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Simplifying cot(3x + -15) = tan(4x + 21) Reorder the terms: cot(-15 + 3x) = tan(4x + 21) (-15 * cot + 3x * cot) = tan(4x + 21) (-15cot + 3cotx) = tan(4x + 21) Reorder the terms: -15cot + 3cotx = ant(21 + 4x) -15cot + 3cotx = (21 * ant + 4x * ant) -15cot + 3cotx = (21ant + 4antx) Solving -15cot + 3cotx = 21ant + 4antx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Reorder the terms: -21ant + -4antx + -15cot + 3cotx = 21ant + 4antx + -21ant + -4antx Reorder the terms: -21ant + -4antx + -15cot + 3cotx = 21ant + -21ant + 4antx + -4antx Combine like terms: 21ant + -21ant = 0 -21ant + -4antx + -15cot + 3cotx = 0 + 4antx + -4antx -21ant + -4antx + -15cot + 3cotx = 4antx + -4antx Combine like terms: 4antx + -4antx = 0 -21ant + -4antx + -15cot + 3cotx = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-21an + -4anx + -15co + 3cox) = 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 '(-21an + -4anx + -15co + 3cox)' equal to zero and attempt to solve: Simplifying -21an + -4anx + -15co + 3cox = 0 Solving -21an + -4anx + -15co + 3cox = 0 Move all terms containing c to the left, all other terms to the right. Add '21an' to each side of the equation. -21an + -4anx + -15co + 21an + 3cox = 0 + 21an Reorder the terms: -21an + 21an + -4anx + -15co + 3cox = 0 + 21an Combine like terms: -21an + 21an = 0 0 + -4anx + -15co + 3cox = 0 + 21an -4anx + -15co + 3cox = 0 + 21an Remove the zero: -4anx + -15co + 3cox = 21an Add '4anx' to each side of the equation. -4anx + -15co + 4anx + 3cox = 21an + 4anx Reorder the terms: -4anx + 4anx + -15co + 3cox = 21an + 4anx Combine like terms: -4anx + 4anx = 0 0 + -15co + 3cox = 21an + 4anx -15co + 3cox = 21an + 4anx 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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