Question

Prove the following trigonometric identity :
$\frac{ \cos( \alpha ) }{1 + \sin( \alpha ) } = \frac{1 - \sin( \alpha ) }{ \cos( \alpha ) }$
Fastest and most correct answer = Brainliest Answer.​

Answer 1

Step-by-step explanation:

LHS=cosa/(1+Sina)

=cosa/1+sina×1-sina/1-sina

=cosa(1-sina)/1-sin^2a

=cosa(1-sina)/cos^2a

=1-sina/cosa

=RHS

Hence Proved

Answer 2

Step-by-step explanation:

$\frac{ \cos( \alpha ) }{ 1 + \sin( \alpha ) }$

$\frac{ \cos( \alpha ) }{ 1 -+ \sin( \alpha ) } \times \frac{1 - \sin( \alpha ) }{1 - \sin( \alpha ) }$

$\frac{ \cos( \alpha )(1 - \sin( \alpha ) }{1 - { \sin( \alpha ) }^{2} }$

$\frac{ \cos( \alpha )(1 - \sin( \alpha ) }{ { \cos( \alpha ) }^{2} }$

$\frac{1 - \sin( \alpha ) }{ \cos( \alpha ) }$