Question

prove that. Am lil bit confuse because i dont understand trigo properly.

Answer 1

$\sqrt{ \frac{1 + \cos( \alpha ) }{1 - \cos( \alpha ) } } \\ \\ = \sqrt{ \frac{(1 + \cos( \alpha ) )\: \: \: (1 + \cos( \alpha ) ) }{(1 - \cos( \alpha ) )(1 + \cos( \alpha )) } } \\ \\ = \sqrt{ \frac{ {(1 + \cos( \alpha )) }^{2} }{ {1 - \cos( \alpha ) }^{2} } } \\ \\ = \sqrt{ \frac{ {(1 + \cos( \alpha )) }^{2} }{ { \sin( \alpha ) }^{2} } } \\ \\ = \frac{1 + \cos( \alpha ) }{ \sin( \alpha ) } \\ \\ = \frac{1}{ \sin( \alpha ) } + \frac{ \cos( \alpha ) }{ \sin( \alpha ) } \\ \\ = \cosec( \alpha ) + \cot( \alpha )$

Answer 2

$Given: \sqrt{ \frac{1+cosA}{1-cosA} }$

$\sqrt{ \frac{1+cosA}{1-cosA} * \frac{1+cosA}{1+cosA} }$

$\sqrt{ \frac{(1+cosA)^2}{1-cos^2A} }$

$\frac{1+cosA}{sinA}$

$\frac{1}{sinA} + \frac{cosA}{sinA}$

cosecA + cotA.


Hope this helps!