In a triangle `A B C ,/_C=pi/2dot` If `tan(A/2)a n dtan(B/2)` are the roots of the equation `a x^2+b x+c=0,(a!=0),` then the value of `(a+b)/c` (where `a , b , c ,` are sides of `` opposite to angles `A , B , C ,` respectively) is

Answer

1

Explanation

`tan ((A)/(2)) + tan ((B)/(2)) = - (b)/(a)`
`tan ((A)/(2)) xx tan ((B)/(2)) = (c ) /(a)`
`A + B = 90^(@) or (A+B)/(2) = 45^(@)`
`rArr tan ((A+B)/(2)) =1= (-(b)/(a))/(1-(c )/(a))`
or `1- (c )/(a) = - (b)/(a)`
or ` a +b = c`
or `(a+b)/(c ) =1`.