Finding an expression for $\tan (a+ b + y)$ which involves only $\tan a, \tan b,$ and $\tan y$.

Question

How to find this ?

I'm stuck at $1$ and how to $1$ to change the tangent associated with a,b or c.

I meant this ,everybody.

$\frac{tan(a)+tan(b)+tan(y)−tan(a)tan(b)tan(y)}{1−tan(a)tan(b)−tan(a)tan(y)−tan(b)tan(y)}$

Answer 1

Let's call $X=\tan(x)$ you have the addition formula $\tan(u+v)=\dfrac{U+V}{1-UV}$

• call $c=a+b$ and develop $\tan(c+y)$
• replace $C$ by $\tan(a+b)$ developpement
• simplify $\dfrac{\frac{A+B}{1-AB}+Y}{1-\frac{A+B}{1-AB}Y}$

Answer 2

I found the appropriate answer. I thought this is misunderstanding of english context and i don't know why? The question from GelfAndSaul Trigonometry Book is

Represent tan(a+b+c) to only representing tan(a),tan(b) and tan(c).

I have an answer but i thought that is wrong.

So this questions means only is we can neglect to 1?