Question

Prove the following trigonometric identities.

`(tan A + tan B)/(cot A + cot B) = tan A tan B`

Answer 1

 We have to prove `(tan A + tan B)/(cot A + cot B) = tan A tan B`

Now

`(tan A + tan B)/(cot A + cot B) = (tan A + tan B)/(1/tan A + 1/tanB)`

`= (tan A + tan B)/((tan B + tan A)/(tan A tan B))`

= tan A tan B

Hence proved.