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Simplifying 0 = sin(7x + 8) + cos(11x + 7) Reorder the terms: 0 = ins(8 + 7x) + cos(11x + 7) 0 = (8 * ins + 7x * ins) + cos(11x + 7) 0 = (8ins + 7insx) + cos(11x + 7) Reorder the terms: 0 = 8ins + 7insx + cos(7 + 11x) 0 = 8ins + 7insx + (7 * cos + 11x * cos) 0 = 8ins + 7insx + (7cos + 11cosx) Reorder the terms: 0 = 7cos + 11cosx + 8ins + 7insx Solving 0 = 7cos + 11cosx + 8ins + 7insx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7cos' to each side of the equation. 0 + -7cos = 7cos + 11cosx + 8ins + -7cos + 7insx Remove the zero: -7cos = 7cos + 11cosx + 8ins + -7cos + 7insx Reorder the terms: -7cos = 7cos + -7cos + 11cosx + 8ins + 7insx Combine like terms: 7cos + -7cos = 0 -7cos = 0 + 11cosx + 8ins + 7insx -7cos = 11cosx + 8ins + 7insx Add '-11cosx' to each side of the equation. -7cos + -11cosx = 11cosx + 8ins + -11cosx + 7insx Reorder the terms: -7cos + -11cosx = 11cosx + -11cosx + 8ins + 7insx Combine like terms: 11cosx + -11cosx = 0 -7cos + -11cosx = 0 + 8ins + 7insx -7cos + -11cosx = 8ins + 7insx Reorder the terms: -7cos + -11cosx + -8ins + -7insx = 8ins + -8ins + 7insx + -7insx Combine like terms: 8ins + -8ins = 0 -7cos + -11cosx + -8ins + -7insx = 0 + 7insx + -7insx -7cos + -11cosx + -8ins + -7insx = 7insx + -7insx Combine like terms: 7insx + -7insx = 0 -7cos + -11cosx + -8ins + -7insx = 0 Factor out the Greatest Common Factor (GCF), '-1s'. -1s(7co + 11cox + 8in + 7inx) = 0 Ignore the factor -1.Subproblem 1
Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing c to the left, all other terms to the right. Add '-1s' to each side of the equation. s + -1s = 0 + -1s Remove the zero: 0 = -1s Simplifying 0 = -1s 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 '(7co + 11cox + 8in + 7inx)' equal to zero and attempt to solve: Simplifying 7co + 11cox + 8in + 7inx = 0 Solving 7co + 11cox + 8in + 7inx = 0 Move all terms containing c to the left, all other terms to the right. Add '-8in' to each side of the equation. 7co + 11cox + 8in + -8in + 7inx = 0 + -8in Combine like terms: 8in + -8in = 0 7co + 11cox + 0 + 7inx = 0 + -8in 7co + 11cox + 7inx = 0 + -8in Remove the zero: 7co + 11cox + 7inx = -8in Add '-7inx' to each side of the equation. 7co + 11cox + 7inx + -7inx = -8in + -7inx Combine like terms: 7inx + -7inx = 0 7co + 11cox + 0 = -8in + -7inx 7co + 11cox = -8in + -7inx 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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