# proofs on trigonometric identities involving complex numbers [duplicate]

Provide a reason for each step of the proof. Prove the identity $$\arctan(1)+\arctan(2)+\arctan(3)=180^{\circ}$$Proof:\begin{align*}\arctan(1)+\arctan(2)+\arctan(3)&=\text{arg}(1+i)+\text{arg}(1+2i)+\text{arg}(1+3i)\\&=\text{arg}\left[(1+i)(1+2i)(1+3i)\right]\\&=\text{arg}(-10)=180^{\circ} \hspace{4cm}\blacksquare\end{align*}

• Take away the right-hand sides of the equations. Step 1 makes it look like you're assuming what you want to prove. – Christopher Carl Heckman Feb 16 '16 at 6:52
• I have edited your post a little. Also, please clarify what is your intention - are you looking for a feedback on your proof? – Galc127 Feb 16 '16 at 6:59
• actually the proof is already given by our professor, and im studying it and i dont fully understand the steps of the proofs, that is why i want a feedback on every steps of the proof and know the reason behind the steps of the proof in our discussions. – aravhinz Feb 16 '16 at 7:23