Question

it is given tan A and tan B are the roots of the equation t^2-pt+q =0.find , in terms of p and q expression for
(a) tan (A+B)
(b) sin^2 (A+B)
(c) cos2(A+B)

Answer 1

\[
t^2-pt+q=(t-\tan{A})(t-\tan{B})=t^2-t(\tan{A}+\tan{B})+\tan{A}\tan{B}\\
p=\tan{A}+\tan{B}=\frac{\sin{A}}{\cos{A}} + \frac{\sin{B}}{\cos{B}}\\
q=\tan{A}\tan{B}=\frac{\sin{A}\sin{B}}{\cos{A}\cos{B}}\\
\text{a. }\tan(A+B)=\frac{\tan{A}+\tan{B}}{1-\tan{A}\tan{B}}=\frac{p}{1-q}\\
\]

Answer 2

plz solve (b) & (c)