$-1 \le \sin x ; \cos x \le 1 \Rightarrow \left\{\begin{matrix} \sin^2 x \ge \sin^5 x & \\ \cos^2 x \ge \cos^7 x & \end{matrix}\right. \Rightarrow 1=\sin^5 x+\cos^7 x \le \sin^2 x+\cos^2 x=1$
Dấu bằng xảy ra khi $\left\{\begin{matrix} \sin^2 x=\sin^5 x& \\ \cos^2 x =\cos^7 x & \end{matrix}\right. ...$