In a `DeltaPQR, angleR=pi/2`. If `tan (P/2)` and `tan(Q/2)` are the roots of `ax^(2)+bx+c=0, a!= 0`, then

Options

A. `a+b=c`
B. `b+c=0`
C. `a+c=b`
D. `b=c`

Answer

A

Explanation

In a triangle `PQR`, ………..
`tan((P)/(3))+tan((Q)/(3))= -(b)/(a) , tan((P)/(3))tan ((Q)/(3)) = (c )/(a)`
Now, `ltR = pi//4 implies P+Q = 3pi//4 implies (P)/(3)+(Q)/(3)= (pi)/(4)`
`:. 1 = tan ((pi)/(4)) = (tan(P//3)+tan(Q//3))/(1-tan(P//3)tan(Q//3))`
`= (-b//a)/(1-c//a) = (-b)/(a-c) implies a+b=c`