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Doctors Medicines MCQs Q&A

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

now multiply
$(sin(alpha)cos(beta))^2 + cancel(cos(alpha)sin(beta)sin(alpha)cos(beta)) - cancel(cos(alpha)sin(beta)sin(alpha)cos(beta))-(cos(alpha)sin(beta))^2 $

then replace the cosine
$sin^2(alpha)(1-sin^2(beta)) -sin^2(beta)(1-sin^2(alpha))$
$= sin^2(alpha) cancel(-sin^2(alpha)sin^2(beta) )-sin^2(beta) + cancel(sin^2(alpha)sin^2(beta))$
$= sin^2(alpha) -sin^2(beta) $

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