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Simplifying sin(2x + -30) + cos(2x + 60) = 0 Reorder the terms: ins(-30 + 2x) + cos(2x + 60) = 0 (-30 * ins + 2x * ins) + cos(2x + 60) = 0 (-30ins + 2insx) + cos(2x + 60) = 0 Reorder the terms: -30ins + 2insx + cos(60 + 2x) = 0 -30ins + 2insx + (60 * cos + 2x * cos) = 0 -30ins + 2insx + (60cos + 2cosx) = 0 Reorder the terms: 60cos + 2cosx + -30ins + 2insx = 0 Solving 60cos + 2cosx + -30ins + 2insx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '30ins' to each side of the equation. 60cos + 2cosx + -30ins + 30ins + 2insx = 0 + 30ins Combine like terms: -30ins + 30ins = 0 60cos + 2cosx + 0 + 2insx = 0 + 30ins 60cos + 2cosx + 2insx = 0 + 30ins Remove the zero: 60cos + 2cosx + 2insx = 30ins Add '-2insx' to each side of the equation. 60cos + 2cosx + 2insx + -2insx = 30ins + -2insx Combine like terms: 2insx + -2insx = 0 60cos + 2cosx + 0 = 30ins + -2insx 60cos + 2cosx = 30ins + -2insx Reorder the terms: 60cos + 2cosx + -30ins + 2insx = 30ins + -30ins + -2insx + 2insx Combine like terms: 30ins + -30ins = 0 60cos + 2cosx + -30ins + 2insx = 0 + -2insx + 2insx 60cos + 2cosx + -30ins + 2insx = -2insx + 2insx Combine like terms: -2insx + 2insx = 0 60cos + 2cosx + -30ins + 2insx = 0 Factor out the Greatest Common Factor (GCF), '2s'. 2s(30co + cox + -15in + inx) = 0 Ignore the factor 2.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 '(30co + cox + -15in + inx)' equal to zero and attempt to solve: Simplifying 30co + cox + -15in + inx = 0 Solving 30co + cox + -15in + inx = 0 Move all terms containing c to the left, all other terms to the right. Add '15in' to each side of the equation. 30co + cox + -15in + 15in + inx = 0 + 15in Combine like terms: -15in + 15in = 0 30co + cox + 0 + inx = 0 + 15in 30co + cox + inx = 0 + 15in Remove the zero: 30co + cox + inx = 15in Add '-1inx' to each side of the equation. 30co + cox + inx + -1inx = 15in + -1inx Combine like terms: inx + -1inx = 0 30co + cox + 0 = 15in + -1inx 30co + cox = 15in + -1inx 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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