Let  $f:R-\{(2n+1)\frac{\pi }{2}:n\in Z\}\to R$  is defined by  $f\left(x\right)=\left({\sec }_{ }^{2}x-ta{n}_{ }^{2}x\right)$.
 $S_1:f$   is periodic function without fundamental period.
$S_2: f$    is continuous at each point in the domain of   f.
$S_3: f$    is differentiable at each point in the domain of  f.
$S_4:\underset{x\to \frac{\pi }{2}}{\lim }f\left(x\right)$  is does not exist.
The number of TRUE statements among the  $S_1,S_2,S_3,S_4$