Khờ Đẹp Zai biến cmn đổi$VT \Leftrightarrow 2sin\frac{A+B}{2}cos\frac{A-B}{2}-\frac{\sqrt{2}}{2}cosC \leq 2sin\frac{A+B}{2}-\frac{\sqrt{2}}{2}cosC=2cos\frac{C}{2}-\frac{\sqrt{2}}{2}cosC=2cos\frac{C}{2}-\frac{\sqrt{2}}{2}\left ( 2cos^2\frac{C}{2}-1 \right )=\sqrt{2}-\sqrt{2}\left( cos\frac{C}{2}-\frac{\sqrt{2}}{2} \right )^2\leq \sqrt{2}$dấu bằng A=B=C/2=45
Khờ Đẹp Zai biến cmn đổi$VT \Leftrightarrow 2\sin\frac{A+B}{2}\cos\frac{A-B}{2}-\frac{\sqrt{2}}{2}\cos C \leq 2\sin\frac{A+B}{2}-\frac{\sqrt{2}}{2}\cos C=2\cos\frac{C}{2}-\frac{\sqrt{2}}{2}\cos C=2\cos\frac{C}{2}-\frac{\sqrt{2}}{2}\left ( 2\cos^2\frac{C}{2}-1 \right )=\sqrt{2}-\sqrt{2}\left( \cos\frac{C}{2}-\frac{\sqrt{2}}{2} \right )^2\le \sqrt{2}$dấu bằng $A=B=C/2=45^0$