simplify the expression sin(x-y)+sin(y-x).
sin(x-y)+sin(y-x) can be simplified by using the fact that sine is an odd function.
Since sin(-θ) = -sin(θ), we can rewrite sin(y-x) as -sin(x-y).
Therefore, the expression simplifies to:
sin(x-y) + (-sin(x-y))
And combining like terms, we get:
sin(x-y) - sin(x-y)
Since the two terms cancel each other out, the simplified expression is:
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