In a triangle ABC , angle C=90 degree , if tan (A/2) and tan (B/2) are the roots of the equation ax^2+bx+c=0 where a is not equal to 0 ,then the correct relationship is

Answers (1)

Solution:    A+B=90^circ    Rightarrow       frac12(A+B)=45^circ

               Now ,      	an (fracA2)+	an(fracB2)=-fracba

                                     	an (fracA2)	an(fracB2)=fracca

                 	herefore          1=	an(fracA+B2)=frac	an fracA2+	anfracB21-	an fracA2 	an fracB2

                  1=	an(fracA+B2)=frac-fracba1-fraccaRightarrow a-c=-b

                    Rightarrow                         c=a+b

 

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