Question

How do you prove `( tan A + tan B) / (1-tan A tan B) = (cot A + cot B ) / ( cot A cot B - 1)`?

Answer 1

We can rewrite the right hand side as follows:

`=(1/tanA + 1/tanB)/(1/tanA1/tanB - 1)`

`=((tanB + tanA)/(tanAtanB))/((1 - tanAtanB)/(tanAtanB)`

`=(tanA + tanB)/(1 - tanAtanB)`

Since the left and right hand sides are equal, the identity has been proved.

Hopefully this helps!