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

cousinhaui

cousinhaui

Answered question

2022-10-29

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

Answer & Explanation

faux0101d

faux0101d

Beginner2022-10-30Added 21 answers

In this way:
arctan 2 + arctan 3 = α
Let's take now the tangent of both members:
tan ( arctan 2 + arctan 3 ) = tan α
tan arctan 2 + tan arctan 3 1 tan arctan 2 tan arctan 3 = tan α
2 + 3 1 2 3 = tan α 5 1 6 = tan α
tan α = 1 α = 3 4 π + k π

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