Given that Tana and tanb are two real roots of the equation x2-4px-3 = 0, and a + B ≠ K π + π / 2, we can find the value of Cos2 (a + b) + PSIN (a + b) cos (a + b)

Given that Tana and tanb are two real roots of the equation x2-4px-3 = 0, and a + B ≠ K π + π / 2, we can find the value of Cos2 (a + b) + PSIN (a + b) cos (a + b)

Because Tana and tanb are two real roots of the equation x2-4px-3 = 0,
So Tana + tanb = 4P, Tana * tanb = - 3,
So tan (a + b) = (Tana + tanb) / (1-tana * tanb) = P,
Original formula = cos ^ 2 (a + b) - Sin ^ 2 (a + b) + PSIN (a + b) cos (a + b)
=[cos^2(a+b)-sin^2(a+b)+psin(a+b)cos(a+b)]/[cos^2(a+b)+sin^2(a+b)]
=[1-tan^2(a+b)+ptan(a+b)]/[1+tan^2(a+b)]
=1/(1+p^2)