Question

If cosec theta = m+n/m-n then find cos theta

Answer 1

$\boxed{SOLUTION \: by \: RKRAUSHAN}$

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Answer 2

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$\csc( \alpha ) = \frac{m + n}{m - n} \\ as \: \csc( \alpha ) = \frac{1}{ \sin( \alpha ) } \\ \sin( \alpha ) = \frac{m - n}{m + n} \\ ( \sin \alpha {}^{2} ) + ( \cos( \alpha ) {}^{2} ) = 1 \\ (\cos( \alpha ) ) {}^{2} = 1 - (\frac{m - n}{m + n}) {}^{2} \\ \cos( \alpha ) = \sqrt{(m + n) {}^{2} -( m - n) {}^{2} } \div m + n \\ \cos( \alpha ) = \sqrt{4mn} \div m + n \\ \cos( \alpha ) = \frac{2 \sqrt{mn} }{m + n}$