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Prove that sin2x - sin2y/cos2y - cos2x = cot(x + y)

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Prove that

\(\cfrac{sin2x\,-\,sin2x}{cos2y\,-\,cos2x}=cot(x\,+\,y)\)

sin2x - sin2y/cos2y - cos2x = cot(x + y)

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Best answer

\(\cfrac{sin2x\,-\,sin2y}{cos2y\,-\,cos2x}\)

= cot(x + y)

Using the formula,

cosA - cosB = -2sin\(\frac{A\,+\,B}{2}\)sin\(\frac{A\,-\,B}{2}\)

sinA - sinB = 2cos\(\frac{A\,+\,B}{2}\)sin\(\frac{A\,-\,B}{2}\)

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