On which of the following intervals, the function $x^{200}+\sin x-1$  is strictly increasing?

$f\text{'}\left(x\right)=200x^{199}+\cos x$

For $x\in \left(0,1\right)$  and $\left(0,\frac{\pi }{2}\right)$

$\cos x$  and $x$  are both positive $\Rightarrow$  $f\left(x\right)$  is increasing

For $x\in \left(\frac{\pi }{2},\pi \right),x>1$  hence $200x^{199}>\cos x$  $\Rightarrow$  $f\left(x\right)$  is increasing