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Simplifying sin(30 + x) + cos(60 + x) = cosx (30 * ins + x * ins) + cos(60 + x) = cosx (30ins + insx) + cos(60 + x) = cosx 30ins + insx + (60 * cos + x * cos) = cosx 30ins + insx + (60cos + cosx) = cosx Reorder the terms: 60cos + cosx + 30ins + insx = cosx Add '-1cosx' to each side of the equation. 60cos + cosx + 30ins + -1cosx + insx = cosx + -1cosx Reorder the terms: 60cos + cosx + -1cosx + 30ins + insx = cosx + -1cosx Combine like terms: cosx + -1cosx = 0 60cos + 0 + 30ins + insx = cosx + -1cosx 60cos + 30ins + insx = cosx + -1cosx Combine like terms: cosx + -1cosx = 0 60cos + 30ins + insx = 0 Solving 60cos + 30ins + insx = 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 + 30ins + -30ins + insx = 0 + -30ins Combine like terms: 30ins + -30ins = 0 60cos + 0 + insx = 0 + -30ins 60cos + insx = 0 + -30ins Remove the zero: 60cos + insx = -30ins Add '-1insx' to each side of the equation. 60cos + insx + -1insx = -30ins + -1insx Combine like terms: insx + -1insx = 0 60cos + 0 = -30ins + -1insx 60cos = -30ins + -1insx Divide each side by '60os'. c = -0.5ino-1 + -0.01666666667ino-1x Simplifying c = -0.5ino-1 + -0.01666666667ino-1x
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