Question

prove cosA/1-sinA=1+sinA/cosA​

Answer 1

Step-by-step explanation:

the explanation is given

Answer 2

To prove :

$\star \: \dfrac{ \cos \: \alpha }{1 - \sin( \alpha ) } = \dfrac{1 + \sin( \alpha ) }{ \cos( \alpha ) }$

Solution:

LHS :

$\leadsto \: \dfrac{ \cos( \alpha) }{1 - \sin( \alpha ) }$

Rationalise the denominator .

$\leadsto \: \dfrac{ \cos( \alpha ) }{1 - \sin( \alpha ) } \times \dfrac{1 + \sin( \alpha ) }{1 + \sin( \alpha ) } \\ \\ \\ \leadsto \: \dfrac{ \cos( \alpha ) (1 + \sin( \alpha )) }{{1}^{2} - { \sin}^{2} \alpha } \\ \\ \leadsto \: \frac{ \cos( \alpha ) (1 + \sin( \alpha )) }{ { \cos}^{2} \alpha }$

Here cos@ gets cancel out .

$\implies \: \dfrac{1 + \sin( \alpha ) }{ \cos( \alpha ) }$

LHS = RHS :

$\huge \blue{ \boxed { \red{\mathfrak{proved}}}}$