求助一道不等式题目，希望提供思路

joker

\(\sqrt{1-(x_{1}y_{1}+x_{2}y_{2}+\dots+x_{n}y_{n})^{2}}\leq \sqrt{1-(x_{1}z_{1}+x_{2}z_{2}+\dots+x_{n}z_{n})^{2}}+\sqrt{1-(z_{1}y_{1}+z_{2}y_{2}+\dots+z_{n}y_{n})^{2}}\)

其中\(x_{1}^{2}+x_{2}^{2}+\dots+x_{n}^{2}=1\)
\(y_{1}^{2}+y_{2}^{2}+\dots+y_{n}^{2}=1\)
\(z_{1}^{2}+z_{2}^{2}+\dots+z_{n}^{2}=1\)

Lwins_G

放到n维欧式空间里去考虑即可。