Question

Prove that
$\frac{ \cos(a) }{1 + \sin(a) } + \frac{1 + \sin(a) }{ \cos(a) } = 2 \sec(a)$
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Answer 1

Answer:

Hope it helps u :)

Step-by-step explanation:

LHS =cos A/(1+sin A) +(1+sin A)/cos A

={cos²A +(1+sin A)²}/cos A.(1+sin A)

={cos²A+1+sin²A+2sin A}/cos A.(1+sin A)

use sin²∅ +cos²∅ =1

=(1+1+2sin A)/cos A(1+sinA)

=2(1+sin A)/cos A(1+sin A)

=2/cos A

=2sec A = RHS

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Answer 2

Step-by-step explanation:

taking LHS

$\frac{cosa}{1 + sina} + \frac{1 + sina}{cosa} \\ \frac{ {(cosa)}^{2} + {(1 + sina)}^{2} } {(1 + sina)(cosa)} \\ \frac{{cos}^{2}a + 1 + {sin}^{2}a + 2sina }{(1 + sina)(cosa)} \\ \frac{{cos}^{2}a + {sin}^{2}a + 1+ 2sina }{(1 + sina)(cosa)} \\ \frac{1 + 1 + 2sina }{(1 + sina)(cosa)} \\ \frac{2 + 2sina }{(1 + sina)(cosa)} \\ \frac{2(1 + sina)}{(1 + sina)(cosa)} \\ \frac{2}{cosa} \\ 2 \times seca \\ 2seca$

hence proved

hope it helps and please mark as brainliest