[tex]cot(\frac{B}{2})=\frac{a+c}{b}[/tex]
<=>[tex]tan(\frac{A+C}{2})=\frac{sinA+sinC}{sinB}[/tex]
<=>[tex]\frac{sin(\frac{A+C}{2})}{cos(\frac{A+C}{2})}= \frac{2sin.(\frac{A+C}{2}).cos(\frac{A-C}{2})}{2.sin(\frac{B}{2}).cos(\frac{B}{2})}[/tex]
<=>[tex]\frac{sin(\frac{A+C}{2})}{cos(\frac{A+C}{2})}= \frac{2sin(\frac{A+C}{2}).sin(\frac{A-C}{2})}{2cos(\frac{A+C}{2}).sin(\frac{A+C}{2})}[/tex]
<=>[tex]\frac{sin(\frac{A+C}{2})}{cos(\frac{A+C}{2})}= \frac{cos(\frac{A-C}{2})}{cos(\frac{A+C}{2})}[/tex]
<=>[tex]sin(\frac{A+C}{2})=cos(\frac{A-C}{2})[/tex]
--> A=90* --> đpcm