Question

Trigonometry， help to prove it

Answer 1

HEY MATE,
here is your answer
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LHS
$= > \: \: \frac{ \cos(a) }{1 + \sin(a) } + \tan(a)$
$= \frac{ \cos(a)(1 - \sin(a)) }{(1 + \sin(a))(1 - \sin(a)) } + \tan(a)$

$=\frac{ \cos(a)(1 - \sin(a)) }{1 - { \sin^{2}(a) } } + \frac{ \sin(a) }{ \cos(a) }$
$= \frac{ \cos(a)(1 - \sin(a)) }{ \cos^{2}(a) } + \frac{ \sin(a) }{ \cos(a) }$
$= \frac{1 - \sin(a) + \sin(a) }{ \cos(a) }$
$= \frac{ 1}{ \cos(a) }$
$= \sec(a)$
=RHS
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Answer 2

Hey friend,
see the answer

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