Question

Prove that cos0/1+sin0+ 1+sin0/cos0=3sec0

Answer 1

Step-by-step explanation:

$\frac{ \cos( \alpha ) }{1 + \sin( \alpha ) } + \frac{1 + \sin( \alpha ) }{ \cos( \alpha ) } \\ = \frac{ { \cos( \alpha ) }^{2} + {(1 + \sin( \alpha ) )}^{2} }{(1 + \sin( \alpha ) ) \cos( \alpha ) } \\ = \frac{ { \cos( \alpha ) }^{2} + 1 + { \sin( \alpha ) }^{2} + 2 \sin( \alpha ) }{(1 + \sin( \alpha ) ) \cos( \alpha ) } \\ = \frac{ { \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} + 1 + 2 \sin( \alpha ) }{(1 + \sin( \alpha ) ) \cos( \alpha ) } \\ = \frac{2 + 2 \sin( \alpha ) }{(1 + \sin( \alpha ) ) \cos( \alpha ) } \\ = \frac{2(1 + \sin( \alpha ) )}{(1 + \sin( \alpha )) \cos( \alpha ) } \\ = \frac{2}{ \cos( \alpha ) } \\ = 2 \sec( \alpha )$