For the sake of periodicity - Part 3

Which of the following statements is/are incorrect?

Statement B : Both the functions $\cos^2 (\sin x)$ and $\cos (\sin x)$ are periodic with the fundamental period $\pi$ .

Statement E : Both the functions $\cos^2 (\sin x)$ and $\cos (\sin x)$ are periodic with the fundamental period $2\pi$ .

Statement S : Both the functions $\sin^2 (\sin x)$ and $\sin (\sin x)$ are periodic with the fundamental period $\pi$ .

Statement T : Both the functions $\sin^2 (\sin x)$ and $\sin (\sin x)$ are periodic with the fundamental period $2\pi$ .