Question

Wanted the Answer to this question with appropriate Steps, Can anyone help??​

Answer 1

Answer:

HENCE PROVED

LHS = RHS

Step-by-step explanation:

$( \csc(90 - \alpha ) - \sin(90 - \alpha ) )( \csc( \alpha ) - \sin( \alpha) ) ( \tan( \alpha ) + \cot( \alpha )) \\ \\ = ( \sec( \alpha ) - \cos( \alpha )) ( \csc( \alpha ) - \sin( \alpha )) ( \tan( \alpha ) + \cot( \alpha )) \\ \\ = ( \frac{1 - { \cos( \alpha ) }^{2} }{ \cos( \alpha ) } )( \frac{1 - { \sin( \alpha ) }^{2} }{ \sin( \alpha ) } )( \frac{ { \cos( \alpha ) }^{2} + { \sin( \alpha ) }^{2} }{ \sin( \alpha ) \cos( \alpha ) } ) \\ \\ = \frac{ { \sin( \alpha ) }^{2} { \cos( \alpha ) }^{2}(1) }{ { \sin( \alpha ) }^{2} { \cos( \alpha ) }^{2} } \\ \\ = 1 = rhs.$