原式即求\( \displaystyle \left( \frac{8}{cos \theta}+\frac{1}{sin \theta} \right)^2 \)
根據廣義柯西
\( \displaystyle \left[ \left( \root 3 \of {\frac{8}{cos \theta}} \right)^3+\left( \root 3 \of {\frac{1}{sin \theta}} \right)^3 \right]
\left[ \left( \root 3 \of {\frac{8}{cos \theta}} \right)^3+\left( \root 3 \of {\frac{1}{sin \theta}} \right)^3 \right]
\left[ \left( \root 3 \of {cos^2 \theta} \right)^3+\left( \root 3 \of {sin^2 \theta} \right)^3 \right] \ge \)
\( \displaystyle \left( \root 3 \of {\frac{8}{cos \theta} \times \frac{8}{cos \theta}\times cos^2 \theta}+
\root 3 \of {\frac{1}{sin \theta}\times \frac{1}{sin \theta} \times sin^2 \theta} \right)^3=5^3=125 \)
