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
$A=B=C/2=45
^0$