Question

prove that
$\sqrt{ \frac{1 + sin \: a}{1 - sin \: a} } = sec \: a + tan \: a$
​

Answer 1

Answer:

Attached photo.

Step-by-step explanation:

Hope this helps.

Answer 2

Step-by-step explanation:

Let us start from the LHS

1-sinA/1+sinA

On rationalising the denominator we get

1-sinA (1-SinA) /1+sinA(1-SinA)

=(1-SinA)²/ 1² -(Sin²A)

=(1-SinA)²/ 1 -(Sin²A)

=(1-SinA)² /Cos² A

=[ 1 -Sin²A = cos²A]

=(1-SinA/CosA)²

=(1/CosA-SinA/CosA)²

=(SecA-tanA)²

= RHS

Hence proved

hope this helps you!!