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Doctors Medicines MCQs Q&A

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You're going to want to expand everything on the right.

$RHS$:

$(sin alpha - cos beta)(sin alpha - cos beta) + (cos beta + sin alpha)(cos beta - sin alpha)$

$sin^2alpha - 2cosbetasinalpha + cos^2beta + cos^2beta -sin^2alpha$

$2cos^2beta - 2cosbetasinalpha$

$2cosbeta(cos beta - sin alpha)$

$-2cosbeta(sin alpha - cos beta)$

The left hand side now equals the right hand side, so the identity has been proved.

Hopefully this helps!

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