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Question
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
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Solution
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
`(cotA + tanB)/(cotB + tanA)`
= `(1/tanA + tanB)/(1/tanB + tanA)`
= `((1 + tanAtanB)/tanA)/((1 + tanAtanB)/tanB) = (1 + tanAtanB)/tanA.tanB/(1 + tanAtanB)`
= `tanB/tanA = 1/tanA.tanB = cotAtanB`
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