If \( \tan \alpha, \tan \beta \) are the roots of the equation \( \mathrm{x} 2+\mathrm{px}+ \) \....

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If \( \tan \alpha, \tan \beta \) are the roots of the equation \( \mathrm{x} 2+\mathrm{px}+ \) \( 1=0 \), then the value of
P
\( \sin ^{2}(\alpha+\beta)+p \sin (\alpha+\beta)+\cos (\alpha+\beta)+q \cos ^{2}(\alpha+\beta) \) is
(1) independent of \( p \) but dependent on \( q \)
(2) independent of \( q \) but dependent on \( p \)
(3) independent of both \( p \) and \( q \)
(4) dependent on both \( p \) and \( q \)


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