Question

Prove the following trigonometric identities.

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

Answer 1

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

Now

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

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

`= cot A/cot B`

`= cot A 1/cot B`

= cot A tan B

Hence proved