Question

prove that 1+cos@÷1-cos=(cosec@+cot)^2​

Answer 1

$= \frac{1 + \cos( \alpha ) }{1 - \cos( \alpha ) } \\ = \frac{1 + \cos( \alpha ) }{1 - \cos( \alpha ) } \times \frac{1 + \cos( \alpha ) }{1 + \cos( \alpha ) } \\ = {(1 + \cos( \alpha ) ) }^{2} \div (1 - \cos {}^{2} ( \alpha ) ) \\ = \frac{( {1 + \cos( \alpha )) }^{2} }{ { \sin( \alpha ) }^{2} } \\ = { (\frac{1 + \cos( \alpha ) }{ \sin( \alpha ) }) }^{2} \\ = { (\frac{1}{ \sin( \alpha ) } + \frac{ \cos( \alpha ) }{ \sin( \alpha ) } ) }^{2} \\ = ( \csc( \alpha ) + \cot( \alpha ) {}^{2}$

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