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