Question

If tan A & tan B are the roots of the quadratic equation, a x² + b x + c = 0 then evaluate a sin² (A + B) + b sin (A + B) . cos (A + B) + c cos² (A + B).

Answer 1

tan A + tan B = - b/a ;  tan A . tan B = c/a

Now E = cos² (A + B) [a tan² (A + B) + b tan (A + B) + c]

E = c