Question

Prove the following identity

Answer 1

$\frac{1 + \tan( \alpha ) }{ \sin( \alpha ) } = \frac{ \frac{1 + \tan( \alpha ) }{ \sin( \alpha ) } }{ \frac{ \sin( \alpha ) }{ \sin( \alpha ) } } = \frac{1}{ \sin( \alpha ) } + \frac{1}{cos( \alpha )} = \sec( \alpha ) + cosec( \alpha )$
Similarly
$\frac{1 + \cot( \alpha ) }{ \cos( \alpha ) } = \frac{ \frac{1 + \cot( \alpha ) }{ \cos( \alpha ) } }{ \frac{ \cos( \alpha ) }{ \cos( \alpha ) } } = \frac{1}{ \cos( \alpha ) } + \frac{1}{ \sin( \alpha ) } = \sec( \alpha ) + cosec( \alpha )$

Adding, we get
2(secA + cosecA)

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Ayush I answered first

Answer 2

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