Question

solve kar do plzzz mate ​

Answer 1

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$\rm \longrightarrow \: \sqrt{ \dfrac{1 + \cos( \theta) }{1 - \cos( \theta) } } + \sqrt{ \dfrac{1 - \cos( \theta) }{1 + \cos( \theta) } }$

Rationalize the denominator ...

$\implies \rm \: \sqrt{ \frac{(1 + \cos( \theta) )(1 - \cos( \theta) )}{(1 - \cos( \theta) )(1 + \cos( \theta)) } } + \sqrt{ \frac{(1 - \cos( \theta))(1 - \cos( \theta)) }{(1 + \cos( \theta))(1 - \cos( \theta)) } }$

$\implies \rm \: \dfrac{1 + \cos( \theta) }{ \sqrt{1 - { \cos }^{2} \theta} } + \dfrac{1 - \cos( \theta) }{ \sqrt{1 - { \cos }^{2} \theta} }$

$\implies \rm \: \dfrac{1 + \cos( \theta) }{ \sqrt{ { \sin}^{2} \theta } } + \dfrac{1 - \cos( \theta) }{ \sqrt{ { \sin }^{2} \theta } }$

$\implies \rm \: \dfrac{1 + \cos( \theta) }{ \sin( \theta) } + \dfrac{1 - \cos( \theta) }{ \sin( \theta) }$

$\implies \rm \: \dfrac{1 + \cos( \theta) + 1 - \cos( \theta) }{ \sin( \theta) }$

$\implies \rm \: \dfrac{2}{ \sin( \theta) }$

$\implies \rm \: 2 \sin( \theta)$

$\therefore\: \rm \: hence \: proved$

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★ Formula Used -

$\mapsto \rm \: (x + y)(x - y) = {x}^{2} - {y}^{2}$

$\mapsto \rm \: 1 - {cos}^{2} \theta \: = \: {sin}^{2} \theta$

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