مثلثية خفيفة مع التصرف

[SIZE=5]SIZE=4]$\LARGE {\color{DarkOrange} sinA+sinB=\frac{-\sqrt{3}}{2}=2sin(\frac{A+B}{2})cos(\frac{A-B}{2})...(1)}$]
${\color{DarkOrange} cosA-cosB=\frac{1}{2}=-2sin(\frac{A+B}{2})sin(\frac{A-B}{2})...(2)}$
$ {\color{DarkOrange} (1)/(2)=cot(\frac{A-B}{2})=\sqrt{3}\rightarrow \frac{A-B}{2}=\frac{\pi}{b}\rightarrow A-B=\frac{\pi}{3}}$

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