Question

PLEASE ANSWER!!!!!!​

Answer 1

Step-by-step explanation:

We have,

$\sin( \alpha )(1 + \tan( \alpha )) + \cos( \alpha ) (1 + \cot( \alpha ))$

$= \tan( \alpha ) ( \sin( \alpha ) + \cos( \alpha )) + \cot( \alpha ) (\sin( \alpha ) + \cos( \alpha ))$

$= ( \sin( \alpha ) + \cos( \alpha ))( \tan( \alpha ) + \cot( \alpha ) )$

$= \frac{ \sin( \alpha ) + \cos( \alpha ) }{ \sin( \alpha ) \cos( \alpha ) }$

$= \sec( \alpha ) + \csc( \alpha )$