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Question

If (1+tan5)(1+tan10)(1+tan15)...(1+tan45)=2k, find the value of 'k' is

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Solution

We have
tan(450x)=1tanx1+tanx
(1+tan(450x))1=1tanx1+tanx
(1+tan(450x))(1+tanx)=2
Consider, (1+tan5)(1+tan10)(1+tan15)...(1+tan45)=2k
(1+tan5)(1+tan40)(1+tan10)(1+tan35)(1+tan15)(1+tan30)(1+tan20)(1+tan25)(1+tan45)=2k
25=2k
k=5

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