Simplify the trigonometric expression $\cos\left(x-y\right)\sin\left(x\right)-\sin\left(x-y\right)\cos\left(x\right)-\sin\left(y\right)$

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Simplify using the identity for the sine of a sum, in reverse: $\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta)=\sin(\alpha\pm \beta)$, where the angle $\alpha$ equals $x$, and the angle $\beta$ equals $x-y$

$\sin\left(x-\left(x-y\right)\right)-\sin\left(y\right)$

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$\sin\left(x-\left(x-y\right)\right)-\sin\left(y\right)$

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression cos(x-y)sin(x)-sin(x-y)cos(x)-sin(y). Simplify using the identity for the sine of a sum, in reverse: \sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta)=\sin(\alpha\pm \beta), where the angle \alpha equals x, and the angle \beta equals x-y. Simplify the product -(x-y). Cancel like terms x and -x. Cancel like terms \sin\left(y\right) and -\sin\left(y\right).

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Main Topic: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.

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