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 October 3rd, 2011, 04:41 AM #1 Newbie   Joined: Sep 2011 Posts: 8 Thanks: 0 arctan Okay so here is the problem. Solve arctan7 + arctan8 and solve it so that you only have one arctan in the final sum. I know how to solve regular arctan but when you add them together it gets tricky. Im stuck here and dont really know what to go. Appreciate all the help I can get and please do explain detailed so that I can understand what you are trying to show me. Thanks beforehand
October 3rd, 2011, 05:02 AM   #2
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Re: arctan

Hello, danneman91!

Quote:
 $\text{Given: }\:\arctan7 \,+\, \arctan8$ $\text{Express in terms of one }\arctan.$

$\text{Recall the identity: }\:\tan(A\,+\,B) \:=\:\frac{\tan A\,+\,\tan B}{1\,-\,\tan A\cdot\tan B}$

$\text{Let: }\:x\;=\;\arctan\,7\,+\,\arctan\,8$

$\text{Take the tangent of both sides: }\:\tan x \;=\;\tan(\arctan\,7\,+\,\arctan\,8)$

$\text{W\!e have: }\:\tan x \;=\;\frac{\tan(\arctan\,7)\,+\,\tan(\arctan\,8)}{ 1\,-\,\tan(\arctan\,7)\cdot\tan(\arctan\,8)} \;=\;\frac{7\,+\,8}{1\,-\,7\cdot8} \;=\;\frac{15}{-55} \;=\;-\frac{3}{11}$

$\text{Therefore: }\:x \;=\;\arctan\left(-\frac{3}{11}\right)$

 October 3rd, 2011, 12:11 PM #3 Newbie   Joined: Sep 2011 Posts: 8 Thanks: 0 Re: arctan Thank you so much for your help soroban. Really appreciate you guys out there who takes the time to help people like me who have a hard time with math.

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