11. The minimum value of the function $y=\sin ^{4} x+\cos ^{4} x+\sec ^{4} x+\csc ^{4} x$ is
11. $8 \frac{1}{2} \quad y \geqslant 2 \sin ^{2} x \cos ^{2} x+2 \sec ^{2} x \cdot \csc x^{2}=2\left(\frac{1}{4} \sin ^{2} 2 x+\frac{4}{\sin ^{2} 2 x}\right)=\frac{1}{2}\left(\sin ^{2} 2 x+\frac{16}{\sin ^{2} 2 x}\right)$, Given that $f(x)=x+\frac{16}{x}$ is monotonically decreasing on $(0,1]$, we know $y \geqslant \frac{1}{2}\left(1+\frac{16}{1}\right)=\frac{17}{2}$, equality holds when $x=k \pi+\frac{\pi}{4}, k \in \mathbf{Z}$.