# tan additions formula expressions only representing with tan [duplicate]

This is expression for $$\tan(a+b+y)$$

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

I want to represent this with only $$\tan(a)$$, $$\tan(b)$$ and $$\tan(y)$$.

Clearly,I want to replace $$1$$ with tan functions of these three variables.

I need this answer because thie is from GelfAndSaul Trigonometry Book questions.Pg-145

## marked as duplicate by zwim, YuiTo Cheng, Claude Leibovici, cmk, ronnoJun 29 at 17:07

• Wait, what are you asking? You want to express it in terms of $\tan (a), \tan (b)$ and $\tan (c)$? You already have an expression in them though. – Amit Rajaraman Jun 29 at 10:18
• Even the $1$? $1 = \tan^0 a$. – peterwhy Jun 29 at 10:21