Question

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cosA/1+sinA. + 1+sinA/cosA =2secA​

Answer 1

Given :

$\frac{cos \: a}{1 + \: sin \: a} + \frac{1 + sin \: a}{cos \: a} = 2 \: sec \: a$

Solution :

L.H.S

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

L. H. S = R. H. S ( Proved)

Using Identity,

sin² a + cos ² a = 1

cos a. sec a = 1

Answer 2

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