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  • 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

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

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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

 

Posted by

Deependra Verma

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