In which one of the following intervals the inequality  $\sin x<\cos x<\cot x$  can hold good?

In the second quadrant,  $\sin x<\cos x$  is false, as  $\sin x$  is positive and   $\cos x$  is negative
In the fourth quadrant,  $\cos x<\cot x$  is false, as  $\cos x$  is positive and  $\cot x$  is negative
Now,  $\sin x<\cos x$  is true in  $(0,\frac{\pi }{4})$   and  $\cos x<\cot x$  is also true.
Further,  $\cos x<\cot x,\text{ as }\cot x=\frac{\cos x}{\sin x}\text{ and }\sin x<1$
In the interval  $(\frac{\pi }{4},\frac{\pi }{2})\sin x>\cos x$