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Simplifying cot(2x) = -1cot(4x + 220) Remove parenthesis around (2x) cot * 2x = -1cot(4x + 220) Reorder the terms for easier multiplication: 2cot * x = -1cot(4x + 220) Multiply cot * x 2cotx = -1cot(4x + 220) Reorder the terms: 2cotx = -1cot(220 + 4x) 2cotx = (220 * -1cot + 4x * -1cot) 2cotx = (-220cot + -4cotx) Solving 2cotx = -220cot + -4cotx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '220cot' to each side of the equation. 220cot + 2cotx = -220cot + 220cot + -4cotx Combine like terms: -220cot + 220cot = 0 220cot + 2cotx = 0 + -4cotx 220cot + 2cotx = -4cotx Add '4cotx' to each side of the equation. 220cot + 2cotx + 4cotx = -4cotx + 4cotx Combine like terms: 2cotx + 4cotx = 6cotx 220cot + 6cotx = -4cotx + 4cotx Combine like terms: -4cotx + 4cotx = 0 220cot + 6cotx = 0 Factor out the Greatest Common Factor (GCF), '2cot'. 2cot(110 + 3x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'cot' equal to zero and attempt to solve: Simplifying cot = 0 Solving cot = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cot = 0 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 '(110 + 3x)' equal to zero and attempt to solve: Simplifying 110 + 3x = 0 Solving 110 + 3x = 0 Move all terms containing c to the left, all other terms to the right. Add '-110' to each side of the equation. 110 + -110 + 3x = 0 + -110 Combine like terms: 110 + -110 = 0 0 + 3x = 0 + -110 3x = 0 + -110 Combine like terms: 0 + -110 = -110 3x = -110 Add '-3x' to each side of the equation. 3x + -3x = -110 + -3x Combine like terms: 3x + -3x = 0 0 = -110 + -3x Simplifying 0 = -110 + -3x 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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