# In a triangle PQR , angle R=pi/2 . if tan (P/2) and tan( Q/2) are the roots of the equation. ax^2+bx +c=0 , then

Solution: $tan P/2+tanQ/2=-b/a ; and tanP/2\times tanQ/2=c/a$

$\\ P+Q+R=\pi \\ \\\Rightarrow P+Q+\pi /2=\pi \Rightarrow P/2+Q/2=\pi /4$

Taking tan both side we get,

$\\ tan(P/2+Q/2)=tan\pi /4\\ \\\Rightarrow tanP/2+tanQ/2/1-tanP/2\times tanQ/2\\ \\\Rightarrow a+b=c$

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