Since, tanA and tanB are roots of the equation 3x2−10x−25=0.
So, tanA+tanB=310 and tanA.tanB=−325
∴tan(A+B)=1−tanA.tanBtanA+tanB=1+325310=2810=145
So, \mathrm{sin}(A+B)=\frac{\pm 5}{\sqrt{221}}&\mathrm{cos}(A+B)=\frac{\pm 14}{\sqrt{221}}
(Note that either both are negative or both positive)
∴3sin2(A+B)−10sin(A+B).cos(A+B)−25cos2(A+B)
=3×22125−22110×5×14−25×221142
=22125(3−28−196)=−25