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If tan A and tan B are the roots of the ...

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

A

`( p ^(2))/({ p^(2) + ( 1-q)^(2) })`

B

`( p^(2))/((p^(2) + q^(2)))`

C

`(q^(2))/({p^(2) - ( 1- q)^(2)})`

D

`(p^(2))/( ( p+q)^(2))`

Text Solution

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The correct Answer is:
A
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