Expressions for tan(x + y + z + w) in terms of tan(x),....

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messa

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Hello, I have this problem, and I don't even know where to start. I don't know what the question is asking, can someone please help me get started on this problem.

Find an expression for tan(x + y + z + w) in terms of tan(x), tan(y), tan(z), and tan(w).
 
Try using the addition formula for tangent.

\(\displaystyle \L\\tan(u+v)=\frac{tan(u)+tan(v)}{1-tan(u)tan(v)}\)

Let u=x+y and v=z+w.

Do it again.
 
tanx+tany+tanz+tanw/1-(tanx+tany)(tanz+tanw)

Is this right? I just plugged the numbers in, but I still don't think it's right.
 
No, that's not correct.

I will start and you finish.

\(\displaystyle \L\\tan(\underbrace{x+y}_{\text{u}}+\underbrace{z+w}_{\text{v}})=tan
(u+v)=\frac{tan(u)+tan(v)}{1-tan(u)tan(v)}\)

\(\displaystyle =\L\\\frac{tan(x+y)+tan(z+w)}{1-tan(x+y)tan(z+w)}\)

Now, expand out again using the addition formula. See?. Each term above can be expressed using the addition formula too. It's a rather cumbersome expression you'll get.
 
okay, that last step you showed me, I've already done, but then I took it a different direction that I guess I shouldn't have. But I expanded the addition formula to this.

tan(x)+tan(y)/1-tan(x)tan(y) + tan(z)+tan(w)/1-tan(z)tan(w) all over 1-tan(x+y)tan(z+w)
 
Good, you're on your way. Except, you didn't use it on the denominator.

You still have it in the form tan(x+y) and tan(z+w).
 
ok so just change finish with the denominator and thats the problem? I don't have to simplify at all?
 
wait, I have another question. Do I have to change the denominator in the numorator as well as the whole denominator?
 
Looks like that's it. Simplify if you like or can.
 
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