## Trigonometry (11th Edition) Clone

$\frac{tan~\alpha}{tan~\beta} = \frac{x}{x+y}$
From the diagram: $tan~\alpha = \frac{x}{z}$ $z = \frac{x}{tan~\alpha}$ $tan~\beta = \frac{x+y}{z}$ $z = \frac{x+y}{tan~\beta}$ We can equate the two expressions for $z$: $\frac{x}{tan~\alpha} = \frac{x+y}{tan~\beta}$ $\frac{tan~\alpha}{tan~\beta} = \frac{x}{x+y}$