Answer
$ 2 \sec^{2} α $
Work Step by Step
Given expression is-
$ \frac{1}{1 - \sin α} + \frac{1}{1 + \sin α} $
= $ \frac{1 + \sin α + 1 - \sin α}{(1 - \sin α)(1 + \sin α)} $
= $ \frac{2}{(1 - \sin^{2} α)} $
= $ 2 . \frac{1}{(\cos^{2} α)} $
( From first Pythagorean identity, $1 - \sin^{2} α$ = $\cos^{2} α$)
= $ 2 \sec^{2} α $
