Question

If tan a=(a)/(a+1) and tan b=(1)/(2a+1) then the value of a+b is

Answer 1

Step-by-step explanation:

tan(A) = a / (a + 1)

tan(B) = 1 / (2a + 1)

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) * tan(B))

(a / (a + 1) + 1 / (2a + 1)) / (1 - (a * 1) / ((a + 1) * (2a + 1))) =>

((a * (2a + 1) + 1 * (a + 1)) / ((a + 1) (2a + 1) - a) =>

(2a^2 + a + a + 1) / (2a^2 + 2a + a + 1 - a) =>

(2a^2 + 2a + 1) / (2a^2 + 2a + 1) =>

1

tan(A + B) = 1

A + B = 45 degrees