If $f$ is a function such that $f\left(x+a\right)=\frac{1+f\left(x\right)}{1-f\left(x\right)}\forall x\in R$, then which of the following is correct?

Let $f\left(x\right)=\sin x+\cos ax$ be a periodic function. Then,

The function $f\left(x\right)=\left|sin4x\right|+\left|cos2x\right|,$ is a periodic function with a fundamental period 

Let $f:R\to R$ be a periodic function such that $f\left(T+x\right)=1+{\left[1-3f\left(x\right)+3{\left(f\left(x\right)\right)}^2-{\left(f\left(x\right)\right)}^3\right]}^{\frac{1}{3}}$, where $T$ is a fixed positive number, then period of $f\left(x\right)$ is