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Simplifying (4tanx + 4)(cosx + -1) = 0 Reorder the terms: (4 + 4antx)(cosx + -1) = 0 Reorder the terms: (4 + 4antx)(-1 + cosx) = 0 Multiply (4 + 4antx) * (-1 + cosx) (4(-1 + cosx) + 4antx * (-1 + cosx)) = 0 ((-1 * 4 + cosx * 4) + 4antx * (-1 + cosx)) = 0 ((-4 + 4cosx) + 4antx * (-1 + cosx)) = 0 (-4 + 4cosx + (-1 * 4antx + cosx * 4antx)) = 0 Reorder the terms: (-4 + 4cosx + (4acnostx2 + -4antx)) = 0 (-4 + 4cosx + (4acnostx2 + -4antx)) = 0 Reorder the terms: (-4 + 4acnostx2 + -4antx + 4cosx) = 0 (-4 + 4acnostx2 + -4antx + 4cosx) = 0 Solving -4 + 4acnostx2 + -4antx + 4cosx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4acnostx2 + -4antx + 4 + 4cosx = 0 + 4 Reorder the terms: -4 + 4 + 4acnostx2 + -4antx + 4cosx = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4acnostx2 + -4antx + 4cosx = 0 + 4 4acnostx2 + -4antx + 4cosx = 0 + 4 Combine like terms: 0 + 4 = 4 4acnostx2 + -4antx + 4cosx = 4 Add '-4cosx' to each side of the equation. 4acnostx2 + -4antx + 4cosx + -4cosx = 4 + -4cosx Combine like terms: 4cosx + -4cosx = 0 4acnostx2 + -4antx + 0 = 4 + -4cosx 4acnostx2 + -4antx = 4 + -4cosx Reorder the terms: -4 + 4acnostx2 + -4antx + 4cosx = 4 + -4cosx + -4 + 4cosx Reorder the terms: -4 + 4acnostx2 + -4antx + 4cosx = 4 + -4 + -4cosx + 4cosx Combine like terms: 4 + -4 = 0 -4 + 4acnostx2 + -4antx + 4cosx = 0 + -4cosx + 4cosx -4 + 4acnostx2 + -4antx + 4cosx = -4cosx + 4cosx Combine like terms: -4cosx + 4cosx = 0 -4 + 4acnostx2 + -4antx + 4cosx = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + acnostx2 + -1antx + cosx) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + acnostx2 + -1antx + cosx)' equal to zero and attempt to solve: Simplifying -1 + acnostx2 + -1antx + cosx = 0 Solving -1 + acnostx2 + -1antx + cosx = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + acnostx2 + -1antx + 1 + cosx = 0 + 1 Reorder the terms: -1 + 1 + acnostx2 + -1antx + cosx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + acnostx2 + -1antx + cosx = 0 + 1 acnostx2 + -1antx + cosx = 0 + 1 Combine like terms: 0 + 1 = 1 acnostx2 + -1antx + cosx = 1 Add '-1cosx' to each side of the equation. acnostx2 + -1antx + cosx + -1cosx = 1 + -1cosx Combine like terms: cosx + -1cosx = 0 acnostx2 + -1antx + 0 = 1 + -1cosx acnostx2 + -1antx = 1 + -1cosx 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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