Trigonometric Identities with Arctangents

John Molokach
January 2, 2012

Five trigonometric identities can be easily observed in the following diagram:

arctan(1) + arctan(2) + arctan(3) = Pi

Here are the identities:

arctan(1) + arctan(2) + arctan(3) = π
arctan(1/2) + arctan(1/3) = π/4
arctan(1) + arctan(1/2) + arctan(1/3) = π/2
arctan(1) + arctan(1/2) = arctan(3)
arctan(1/3) + arctan(1) = arctan(2).

Do you see them all?

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