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Question

If (1+tanα)(1+tan4α)=2, αϵ(0,π/16) then α is equal to

A
π20
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B
π30
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C
π40
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D
π60
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Solution

The correct option is B π20
(1+tanα)(1+tan4α)=2
1+tanα.tan4α+tanα+tan4α=2
tanα+tan4α=1tanα.tan4α
tanα+tan4α1tanα.tan4α=1
tan5α=15α=π4α=π20

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