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Question Number 126381 by liberty last updated on 20/Dec/20

$$\arctan 1+\arctan 2+\arctan 3=?$$

Answered by benjo_mathlover last updated on 20/Dec/20

$$(\bullet )\arctan 1+\arctan 2=\arctan \left(\frac{1+2}{1-1.2}\right)$$$$\arctan (-3)$$$$(\bullet \bullet )\arctan (-3)+\arctan \left(3\right)=\arctan \left(\frac{-3+3}{1-(-3)\left(3\right)}\right)$$$$=\arctan \left(\frac{0}{7}\right)=\arctan 0=\pi$$

Commented by talminator2856791 last updated on 20/Dec/20

$$\mathrm{brilliant}$$

Commented by mathmax by abdo last updated on 20/Dec/20

$$\arctan \left(0\right)=0$$

Commented by liberty last updated on 20/Dec/20

$$correct...answeris\pi$$

Answered by mathmax by abdo last updated on 20/Dec/20

$$\arctan \left(1\right)=\frac{\pi }{4}\mathrm{and}\tan (\arctan 2+\arctan 3)=\frac{2+3}{1-2.3}=\frac{5}{-5}=-1$$$$\Rightarrow \arctan 2+\arctan 3=\arctan (-1)=-\frac{\pi }{4}\Rightarrow \mathrm{\Sigma }\arctan =0$$

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