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

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Answer 1 · 2018-04-09T04:15:17

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!

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