Value of

tan9°+ tan36° + tan9°tan36°

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Solution

As tan 45 = 1 = tan ( 36 + 9 ) = 1

= ( tan 36 + tan 9 ) / ( 1 - tan 9 tan 36 ) = 1

= tan 36 + tan 9 = 1 - tan 9 tan 36

= tan 36 + tan 6 + tan 9 tan 36 = 1

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