# What formula or rule has been used here?

I was in between proving a trigonometric identity but couldn't succeed. I went through the solution and saw this in between

\begin{align}\frac{\cos A \cos B}{\sin A \sin B}&= \frac{3}{1}\\\\ \frac{\cos A \cos B +\sin A \sin B}{\cos A \cos B - \sin A \sin B}&= \frac{3+1}{3-1}\end{align}

What happened there in the second step?

• Jul 17 '17 at 10:28

If we have $$\frac xy = \frac31$$ then this means, by definition of fractions, that $x = 3y$. This yields $$\frac{x+y}{x-y} =\frac{3y+y}{3y-y} = \frac{3+1}{3-1}$$ In your case, $x = \cos A\cos B$ and $y = \sin A\sin B$.