1.

√1-cosA/1+cosA=cosecA-cotA prove it

Answer»

Step-by-step EXPLANATION:

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


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