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Simplifying (2cosx + 1)(3sinx + 3) = 0 Reorder the terms: (1 + 2cosx)(3sinx + 3) = 0 Reorder the terms: (1 + 2cosx)(3 + 3insx) = 0 Multiply (1 + 2cosx) * (3 + 3insx) (1(3 + 3insx) + 2cosx * (3 + 3insx)) = 0 ((3 * 1 + 3insx * 1) + 2cosx * (3 + 3insx)) = 0 ((3 + 3insx) + 2cosx * (3 + 3insx)) = 0 (3 + 3insx + (3 * 2cosx + 3insx * 2cosx)) = 0 Reorder the terms: (3 + 3insx + (6cinos2x2 + 6cosx)) = 0 (3 + 3insx + (6cinos2x2 + 6cosx)) = 0 Reorder the terms: (3 + 6cinos2x2 + 6cosx + 3insx) = 0 (3 + 6cinos2x2 + 6cosx + 3insx) = 0 Solving 3 + 6cinos2x2 + 6cosx + 3insx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 6cinos2x2 + 6cosx + -3 + 3insx = 0 + -3 Reorder the terms: 3 + -3 + 6cinos2x2 + 6cosx + 3insx = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 6cinos2x2 + 6cosx + 3insx = 0 + -3 6cinos2x2 + 6cosx + 3insx = 0 + -3 Combine like terms: 0 + -3 = -3 6cinos2x2 + 6cosx + 3insx = -3 Add '-3insx' to each side of the equation. 6cinos2x2 + 6cosx + 3insx + -3insx = -3 + -3insx Combine like terms: 3insx + -3insx = 0 6cinos2x2 + 6cosx + 0 = -3 + -3insx 6cinos2x2 + 6cosx = -3 + -3insx Reorder the terms: 3 + 6cinos2x2 + 6cosx + 3insx = -3 + -3insx + 3 + 3insx Reorder the terms: 3 + 6cinos2x2 + 6cosx + 3insx = -3 + 3 + -3insx + 3insx Combine like terms: -3 + 3 = 0 3 + 6cinos2x2 + 6cosx + 3insx = 0 + -3insx + 3insx 3 + 6cinos2x2 + 6cosx + 3insx = -3insx + 3insx Combine like terms: -3insx + 3insx = 0 3 + 6cinos2x2 + 6cosx + 3insx = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 2cinos2x2 + 2cosx + insx) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 2cinos2x2 + 2cosx + insx)' equal to zero and attempt to solve: Simplifying 1 + 2cinos2x2 + 2cosx + insx = 0 Solving 1 + 2cinos2x2 + 2cosx + insx = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2cinos2x2 + 2cosx + -1 + insx = 0 + -1 Reorder the terms: 1 + -1 + 2cinos2x2 + 2cosx + insx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2cinos2x2 + 2cosx + insx = 0 + -1 2cinos2x2 + 2cosx + insx = 0 + -1 Combine like terms: 0 + -1 = -1 2cinos2x2 + 2cosx + insx = -1 Add '-1insx' to each side of the equation. 2cinos2x2 + 2cosx + insx + -1insx = -1 + -1insx Combine like terms: insx + -1insx = 0 2cinos2x2 + 2cosx + 0 = -1 + -1insx 2cinos2x2 + 2cosx = -1 + -1insx 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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