Question

if tan A = 1/3 and tan (b/2)= 1/2 then tan (a+b)​

Answer 1

Answer:

Given: tan(A+B) = 1/2 and tan(A-B) = 1/3,

Now let A+B = X and A-B = Y i.e tan(X) = 1/2 and tan(Y) = 1/3,

2A = (A+B) + (A-B) = X + Y,

=> tan(2A) = tan(X+Y) = [tan(X) + tan(Y)]/[1 - tan(X).tan(Y)],

= (1/2 + 1/3)/[1 - (1/2).(1/3)],

= (5/6)/(5/6) = 1