Question

prove that cosA/1+sinA + 1+sinA/cosA = 2secA​

Answer 1

Answer:

Step-by-step explanation:

1+sinA/cosA + cosA/1+sinA

=(1+sinA)/cosA+cosA/1+sinA.1-sinA/1-sinA

=1+sinA/cosA+cosA(1-sinA)/cos^A

=1+sinA/cosA+1-sinA/cosA

=2/cosA

=2secA

Answer 2

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$\frac{ \cos \: a }{1 + \sin \: a} + \frac{1 + \sin \: a }{ \cos \: a }$

$\frac{ { \cos }^{2}a + {(1 + \sin \: }^{2} a) + 1 + 2 \sin \: a }{(1 + \sin \: a) \cos \: a }$

$\frac{1 + 1 + 2 \sin \: a }{(1 + \sin \: a) \cos \: a }$

$\frac{2(1 + \sin \: a) }{(1 + \sin \: a) \cos \: a }$

$\frac{2}{ \cos \: a }$

$2 \sec \: a$

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