# What formula or rule has been used here?

by mettled mike   Last Updated July 17, 2017 10:20 AM

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

$\frac{\cos A \cos B}{\sin A \sin B}= \frac{3}{1}$

$\frac{\cos A \cos B +\sin A \sin B}{\cos A \cos B - \sin A \sin B}= \frac{3+1}{3-1}$

What happened there in the second step?

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