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Q.

The value of tan5∘tan10∘tan15∘⋯tan85∘is


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a

0

b

    Not defined

c

1

d

-1  

answer is C.

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Detailed Solution

Given expression is tan5∘tan10∘tan15∘⋯tan85∘.
We know, tanx=cot(90∘-x) and tanx.cotx=1.
We get,
tan5.tan10.tan15…tan80.tan85.
=tan5.tan10.tan15…tan45.cotcot 90-35…cotcot 90-10 cot 90-5
After rearranging terms,
=tan5.cot5.tan10.cot10...tan45=1.
Hence, the correct option is (3).
 
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