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Question
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Solution
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.
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