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The value of (tan1 tan2 tan3 ... tan89 ) is

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$\tan 1^0 \tan 2^0 \tan 3^0 ... \tan 89^0 \\ =\tan 1^0 \tan 2^0 \tan 3^0 ..\tan 44^0 \tan 45^0 \tan 46^0 ... \tan 89^0 \\ =\tan 1^0 \tan 2^0 \tan 3^0 ..\tan 44^0 \tan 45^0 \tan (90-44)^0 ... \tan (90-1)^0 \\ \because \tan (90-A) = \cot A \\\\ =\tan 1^0 \tan 2^0 \tan 3^0 ..\tan 44^0 \tan 45^0 \cot 44^0 ... \cot 1^0 \\ = 1$

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Ravindra Pindel

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