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#.