How do you find the exact value of $arctan(2) + arctan(3)$ ?

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Answer 1 · 2015-05-25T16:17:45

In this way:

$arctan2+arctan3=alpha$ .

Let's take now the tangent of both members:

$tan(arctan2+arctan3)=tanalpharArr$

$(tanarctan2+tanarctan3)/(1-tanarctan2tanarctan3)=tanalpharArr$

$(2+3)/(1-2*3)=tanalpharArr5/(1-6)=tanalpharArr$

$tanalpha=-1rArralpha=3/4pi+kpi$ .

How do you find the exact value of arctan(2) + arctan(3)arctan(2) + arctan(3)?