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Prove the identity:

(sin⁡(2x-y)+sin⁡y)/(cos⁡(2x-y)+cos⁡y )=tan⁡x

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Recall your sum/difference formulas. You have

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

Now just divide and you have tan(x)

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