Question

prove that
$\frac{ \sin( \alpha ) }{1 - \cos( \alpha ) } + \frac{1 + \cos( \alpha ) }{ \sin( \alpha ) } = 2cosec \alpha$
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Answer 1

Step-by-step explanation:

hey mate here is ur answer...one thing u have to correct in the question...if 1+cos alpha ..then the another is also be + not - ..if we consider - then we get different ansr ..so correct the question...

Answer 2

Answer

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Dividing numerator and denominator by sin θ

$\tt \: ⇒\frac{ \frac{2 \sin( \alpha ) - \cos( \alpha ) }{ \sin( \alpha ) } }$. ${ \frac{ \cos( \alpha ) + \sin( \alpha ) }{ \sin( \alpha ) } } = 1</p><p>⇒ </p><p>sin(α)/</p><p>cos(α)+sin(α)$

sin(α)

2sin(α)−cos(α)

=1

$\tt⇒ \frac{2 - \cot( \alpha ) }{1 + \cot( \alpha ) } = 1⇒ </p><p>1+cot(α)/2−cot(α)$

$\tt \: ⇒2 - \cot( \alpha ) = 1 + \cot( \alpha )⇒2−cot(α)=1+cot(α)$

$\tt \: ⇒ \cot( \alpha ) = \frac{1}{2}⇒cot(α)= 1/2$

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Hope it's Helpful.....:)