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Sum it Square it

Geometry Level 3

If $\tan A, \tan B$ are roots of $x^{2} - Px + Q = 0$ the value of $\sin^{2}(A+B)$ is?

Note: $P,Q$ are real numbers.

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\frac{P^{2}}{P^{2} + (1-Q)^{2}}

\frac{P^{2}}{P^{2} + Q^{2}}

\frac{P^{2}}{(P + Q)^{2}}

\frac{P^{2}}{Q^{2} + (1-Q)^{2}}

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by Harshvardhan Mehta

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