Question

How do you evaluate `Arctan(1/2)+arctan(1/3)`?

Answer 1

`arc tan 1`=pi/4, the principal against the principal values. The general value is `npi+pi/4, n=0, +-1, +-2. +-3,...`

Explanation:

Use tan ( a + b )=( tan a + tan b )/( 1 - tan a tan b).

Here, the tangent of the sum of the angles #=(1/2+1/3)/(1-(1/2)(1/3))=1.

Answer is the inverse `tan^(-1) 1`. Now, see the answer. again.