If the extreme value of the function $f(x)=\frac{4}{\sin x}+\frac{1}{1-\sin x}$ in $\left[0, \frac{\pi}{2}\right]$ is $m$ and it exists at $x=k$, then $\cos k=$

If the normal drawn at the point $P$ on the curve $y=x \log x$ is parallel to the line $2 x-2 y=3$, then $P=$

If the curves $y^2=16 x$ and $9 x^2+\alpha y^2=25$ intersect at right angles, then $\alpha=$

If the function $y=\sin x(1+\cos x)$ is defined in the interval $[-\pi, \pi]$, then $y$ is strictly increasing in the interval