Question 888244
Find the value of tan1 tan2 tan3 .... tan89

Solution:

 tan1 = cot89;tan2 = cot88...

Thus, we get 44 pairs of tan x cot,thereby giving you 1 as tan is the reciprocal of cot.
One that is left out alone is tan45. 
But we know tan45 = 1. 
Hence,the answer to this question is 1.