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  • 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

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

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Solution: tan P/2+tanQ/2=-b/a ; and tanP/2 imes 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)=tanpi /4\ \Rightarrow tanP/2+tanQ/2/1-tanP/2 imes tanQ/2\ \Rightarrow a+b=c

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Deependra Verma

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