Author Topic: Simplify... (Read 719 times) Tweet Share

Mao · « **on:** July 25, 2008, 04:33:27 pm »

on the SAC today, I was presented with this question:

$\mbox{Simplify }\tan(x+y)-\tan(x)$

looks rather easy, until you dive into it. Of the different methods, none came up "simpler" than this original solution.
now that the SAC's gone, I am wondering how would you go about doing that?

these three are my end solutions:

$\frac{\tan(y)\sec^2(x)}{1-\tan(x)\tan(y)}$ , and consequently $\frac{\sec^2(x)}{\cot(y)-\tan(x)}$

or alternatively $\frac{\sin(y)}{\cos(x)\cos(x+y)}$

simple? I don't think so...

dcc · « **Reply #1 on:** July 25, 2008, 11:45:40 pm »

$\mbox{Simplify }\tan(x+y)-\tan(x)$

I would imagine that they would prefer the form $\tan \left(x + y\right) - \tan \left(x\right) = \dfrac{\sin \left(y\right)}{\cos \left(x\right) \cos \left(x + y\right)}$

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Author Topic: Simplify... (Read 719 times) Tweet Share

Mao

Simplify...

dcc

Re: Simplify...

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