9) $\Leftrightarrow 2\cos^2A-4\sqrt{2}\sin \frac{A}{2}\cos \frac{B-C}{2}-4=0$
$\Rightarrow 0\le 2(1-2x^2)-4\sqrt{2}x-4=-2(\sqrt{2}x-1)^2$
với $x=\sin \frac{A}{2}$
$\sin \frac{A}{2}=\frac{\sqrt{2}}{2}\Rightarrow \frac{\widehat{A}}{2}= \frac{\Pi }{4}\Rightarrow \widehat{A}=\frac{ \Pi }{2}$
$\widehat{B}=\widehat{C}= \frac{\Pi }{4}$
12) $\Leftrightarrow [cos(A-B)+cosC](1-cosC)=1$
$VT\leq (1+cosC)(1-cosC)=1-cos^2C=sin^2C\leq 1$
Suy ra .......
14) $\Leftrightarrow \left(\frac{1}{\sqrt{2}}sinB - \sqrt{\frac{3}{2}}sinC \right)^{2} + \left(\frac{1}{\sqrt{2}}cosB + \sqrt{\frac{3}{2}}cosC - \sqrt{2} \right)^{2} = 0$.
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
