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