Question

if A and B are acute angle such that tan A = 1/2,tanB=1/3and tan (A+B) = TanA +tan B / 1-tanA tanB ,find (A+B) .Hence find sin^2 (A+B) + cos^ -(A +B)

Answer 1

tan (A+B)= 5/6 / 5/6
tan(A+B) = 1

A+B = 45 degree

then sin square (A+B) + cos square ( A+B)

= 1/2 + 1/2
= 1