Question

If A+B+C=180 then prove that,
cot2A.cot2B + cot2B.cot2C + cot2C.cot2A =1

Answer 1

i think this is what you are looking for:

https://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities#Miscellaneous_--_the_triple_tangent_identity

your equation may have a typo, the cot shouldn't be squared

Answer 2

\[\cot A \cot B + \cot B \cot C + \cot A \cot C = 1\]
\[\frac{1}{\tan A \tan B} + \frac{1}{\tan B \tan C} + \frac{1}{\tan A \tan C} = 1\]
\[\frac{\tan A + \tan B + \tan C}{\tan A \tan B \tan C} = 1\]