Question

(cot theta- cosec theta)²​

Answer 1

Step-by-step explanation:

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