#### Answer

The given equation is NOT an identity.

#### Work Step by Step

Use a graphing utility to graph $y=\dfrac{1}{1+\sin{x}}+\dfrac{1}{1-\sin{x}}$ and $y=\sec^2{x}$.
(Refer to the graphs below.)
Note that the graphs are different from each other
This means that the given equation is not an identity.