Question

If tan(A+B)=8 and tan B = 1/57 find tan A
Step by Step Please

Answer 1

We can use the identity:

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

Substitute the given values:

8 = (tan A + (1/57))/(1 - (1/57)*tan A)

Multiplying both sides by (1- (1/57)*tan A), we get:

8(1 - (1/57)*tan A) = tan A + (1/57)

Expanding and simplifying, we get:

8 - (8/57)*tan A = tan A + (1/57)

Bringing terms with tan A to one side, we get:

(8/57 + 1/57) = (9/57)*tan A

tan A = (9/57)*(58/8)

tan A = 9/4

Therefore, tan A = 2.25 (approx)