# If $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0,$ then $\sin^2 (A+B)$=

$\begin {array} {1 1} (a)\;\frac{p^2}{p^2+q^2} & \quad (b)\;\frac{p^2}{(p+q)^2} \\ (c)\;1-\frac{p}{(1-q)^2} & \quad (d)\;\frac{p^2}{p^2+(1-q)^2} \end {array}$

$(d)\;\frac{p^2}{p^2+(1-q)^2}$