Question

Verificar la identidad de:
(tanx+cotx)(cosx+senx)=cosx+secx

Answer 1

$( \tan(x) + \cot(x) )( \cos(x) + \sin(x)) \\ = (\frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) } )( \cos(x) + \sin(x) ) \\ = (\frac{ \sin(x) \sin(x) + \cos(x) \cos(x) }{ \cos(x) \sin(x) } )( \cos(x) + \sin(x) )$
$= (\frac{ { \sin(x) }^{2} + { \cos(x) }^{2} }{ \cos(x) \sin(x) })( \cos(x) + \sin(x) ) \\ = \frac{1}{ \cos(x) \sin(x) } ( \cos(x) + \sin(x) ) \\ = \frac{ \cos(x) }{ \cos(x) \sin(x) } + \frac{ \sin(x) }{ \cos(x) \sin(x) } \\ = \frac{1}{ \sin(x) } + \frac{1}{ \cos(x) }$
= secx+ cscx