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Question

tanπ5+2tan2π5+4cot4π5=

A
cotπ5
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B
cot2π5
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C
cot3π5
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D
cot4π5
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Solution

The correct option is A cotπ5
tanπ5+2tan2π5+4cot4π5
Add and subtract cotπ5
=cotπ5cotπ5+tanπ5+2tan2π5+4cot4π5
Apply this formula cotxtanx=2×cot2x
=cotπ54cot4π5+4cot4π5
=cotπ5

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