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Simplifying cos(4x + 2) + 3sin(2x + 1) = 2 Reorder the terms: cos(2 + 4x) + 3sin(2x + 1) = 2 (2 * cos + 4x * cos) + 3sin(2x + 1) = 2 (2cos + 4cosx) + 3sin(2x + 1) = 2 Reorder the terms: 2cos + 4cosx + 3ins(1 + 2x) = 2 2cos + 4cosx + (1 * 3ins + 2x * 3ins) = 2 2cos + 4cosx + (3ins + 6insx) = 2 Solving 2cos + 4cosx + 3ins + 6insx = 2 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3ins' to each side of the equation. 2cos + 4cosx + 3ins + -3ins + 6insx = 2 + -3ins Combine like terms: 3ins + -3ins = 0 2cos + 4cosx + 0 + 6insx = 2 + -3ins 2cos + 4cosx + 6insx = 2 + -3ins Add '-6insx' to each side of the equation. 2cos + 4cosx + 6insx + -6insx = 2 + -3ins + -6insx Combine like terms: 6insx + -6insx = 0 2cos + 4cosx + 0 = 2 + -3ins + -6insx 2cos + 4cosx = 2 + -3ins + -6insx Reorder the terms: -2 + 2cos + 4cosx + 3ins + 6insx = 2 + -3ins + -6insx + -2 + 3ins + 6insx Reorder the terms: -2 + 2cos + 4cosx + 3ins + 6insx = 2 + -2 + -3ins + 3ins + -6insx + 6insx Combine like terms: 2 + -2 = 0 -2 + 2cos + 4cosx + 3ins + 6insx = 0 + -3ins + 3ins + -6insx + 6insx -2 + 2cos + 4cosx + 3ins + 6insx = -3ins + 3ins + -6insx + 6insx Combine like terms: -3ins + 3ins = 0 -2 + 2cos + 4cosx + 3ins + 6insx = 0 + -6insx + 6insx -2 + 2cos + 4cosx + 3ins + 6insx = -6insx + 6insx Combine like terms: -6insx + 6insx = 0 -2 + 2cos + 4cosx + 3ins + 6insx = 0 The solution to this equation could not be determined.
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