If tan A and tan B are the roots of the quadr | vedclass

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(D) Given that $	an A$ and $	an B$ are the roots of the quadratic equation $x^2-px+q=0$. From the properties of roots,we have: $	an A + 	an B = p$

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

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(D) Given that $	an A$ and $	an B$ are the roots of the quadratic equation $x^2-px+q=0$. From the properties of roots,we have: $	an A + 	an B = p$ $	an A 	an B = q$ Using the formula for $	an(A+B)$: $	an(A+B) = \frac{	an A + 	an B}{1 - 	an A 	an B} = \frac{p}{1-q}$ Now,consider a right-angled triangle where the opposite side is $p$ and the adjacent side is $(1-q)$. The hypotenuse is $\sqrt{p^2 + (1-q)^2}$. Therefore,$\sin(A+B) = \frac{p}{\sqrt{p^2 + (1-q)^2}}$. Squaring both sides,we get: $\sin^2(A+B) = \frac{p^2}{p^2 + (1-q)^2}$.

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

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