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The Value of logtan10+logtan20+⋯⋯+logtan890 is

Correct Answer: 0

Explanation:

=   log   tan 1 0 + log   tan 89 0   +   log   tan 2 0 +   log   tan 88 0 + + log   tan 45 0   


 


=   log   [ tan 1 0   ×   tan 89 0 ]   +   log   [ tan 2 0   ×   tan 88 0   ]   + + log 1   


 


  tan ( 90 - θ ) = c o t θ   a n d   tan   45 0 = 1   


 


= log 1 + log 1 +.....+log 1 


 


= 0.


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