How do you simplify $cot (x + y) - sin (x + 2 y)$ $cot(x+y)-sin(x+2y)$ to trigonometric functions of x and y?

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Answer 1 · 2016-08-10T15:42:08

$cos (x + y) - sin (x + 2 y)$ $cos(x+y)-sin(x+2y)$

$= cos x cos y - sin x sin y - sin x cos 2 y - cos x sin 2 y$ $=cosxcosy-sinxsiny-sinxcos2y-cosxsin2y$

$= cos x cos y - sin x sin y - sin x (2 {cos}^{2} y - 1) - 2 cos x sin y cos y$ $=cosxcosy-sinxsiny-sinx(2cos^2y-1)-2cosxsinycosy$

$= cos x cos y - sin x sin y - 2 sin x {cos}^{2} y + sin x - 2 cos x sin y cos y$ $=cosxcosy-sinxsiny-2sinxcos^2y+sinx-2cosxsinycosy$

How do you simplify cot(x+y)-sin(x+2y)cot(x+y)−sin(x+2y)cot(x+y)-sin(x+2y) to trigonometric functions of x and y?