If P is a predicate then $ \sim P $ is It is not the case that P or simply Not P
Let $P$: Some trigonometric function are not periodic, it means there exists a function which is Trigonometric and not Period
It is written as $\exists x(T(x) \land \sim P(x))$
Now It is not the case that some trigonometric function are not periodic is $\sim P$ which is written as $ \sim \exists x(T(x) \land \sim P(x))$
Hence option A) is correct