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Simplifying cos(45 + -1x) = 2sin(30 + x) (45 * cos + -1x * cos) = 2sin(30 + x) (45cos + -1cosx) = 2sin(30 + x) 45cos + -1cosx = (30 * 2ins + x * 2ins) 45cos + -1cosx = (60ins + 2insx) Solving 45cos + -1cosx = 60ins + 2insx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Reorder the terms: 45cos + -1cosx + -60ins + -2insx = 60ins + -60ins + 2insx + -2insx Combine like terms: 60ins + -60ins = 0 45cos + -1cosx + -60ins + -2insx = 0 + 2insx + -2insx 45cos + -1cosx + -60ins + -2insx = 2insx + -2insx Combine like terms: 2insx + -2insx = 0 45cos + -1cosx + -60ins + -2insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(45co + -1cox + -60in + -2inx) = 0Subproblem 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 '(45co + -1cox + -60in + -2inx)' equal to zero and attempt to solve: Simplifying 45co + -1cox + -60in + -2inx = 0 Solving 45co + -1cox + -60in + -2inx = 0 Move all terms containing c to the left, all other terms to the right. Add '60in' to each side of the equation. 45co + -1cox + -60in + 60in + -2inx = 0 + 60in Combine like terms: -60in + 60in = 0 45co + -1cox + 0 + -2inx = 0 + 60in 45co + -1cox + -2inx = 0 + 60in Remove the zero: 45co + -1cox + -2inx = 60in Add '2inx' to each side of the equation. 45co + -1cox + -2inx + 2inx = 60in + 2inx Combine like terms: -2inx + 2inx = 0 45co + -1cox + 0 = 60in + 2inx 45co + -1cox = 60in + 2inx 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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