Question

Prove the following trigonometric identities.

`1/(1 + sin A) + 1/(1 - sin A) =  2sec^2 A`

Answer 1

We have to prove `1/(1 + sin A) + 1/(1 - sin A) =  2sec^2 A`

We know that, `sin^2 A + cos^2 A = 1`

So, 

`1/(1 + sin A) + 1/(1 - sin A) =((1 - sin A) + (1 + sin A))/((1 + sin A)(1 - sin A))`

`= (1 - sin A + 1+ sin A)/(1 - sin^2 A)`

`= 2/cos^2 A`

`= 2 sec^2 A`