Maths:Trigonometry!?

Question

Find the exact value of tan^(-1)2+tan^(-1)3.
Can anyone show me how to do this step by step.
Thanks a lot.

Yes.its inverse tangent2 + inverse tangent3.
Find the exact value without the use of a calculator.

Answer 1

You seem to have some pretty pathetic answers.

Let A = arctan 2 and B = arctan 3.

As noted, tan (A+B) = (tan A + tan B) / (1 - tan A tan B)
but the previous answerers haven't been able to substitute correctly:
= (2 + 3) / (1 - 2*3)
= 5 / -5
= -1.
So A+B = -π/4 + kπ for some integer k.
Now we know A and B will both be in the interval (π/4, π/2), so A+B will be in the interval (π/2, π). So the answer is 3π/4.

Answer 2

Is the question "Find the exact value of tangent inverse of 2 + tangent inverse of 3"?

Answer 3

using tan(A+B) = (tan A + tan B)/(1-tan A tan B)
we get tan((tan^1 2 + tan ^ -1 3)) = (2+3)/(1-1/2*1/3) = 5/(1-1/6)
= 6
so we have tan ^1 (6)

Answer 4

let A = tan^(-1)(2) and B = tan^(-1) (3)
tan A = 2 and tan B = 3
tan(A + B) = (tan A + tan B) / (1 - tan A.tan B)
tan(A + B) = (2 + 3) / (-5/6) = - 6
A + B = tan^(-1) (- 6)
tan^(-1).2 + tan^(-1).3 = tan^(-1).(- 6)