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`(Tan a + Tanb )/(Cot a + Cot B) = Tan a Tan B`

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Question

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

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Solution

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

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

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

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

        = ๐‘ก๐‘Ž๐‘›๐ด ๐‘ก๐‘Ž๐‘›๐ต
        = RHS
Hence, LHS = RHS

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