If (1+tan⁡α)(1+tan⁡4α)=2,α∈(0,π16) then α=

A+B=π4 then (1+tan⁡A)(1+tan⁡B)=2⇒α+4α=π4⇒5α=π4⇒α=π20

If (1+tan⁡α)(1+tan⁡4α)=2,α∈(0,π16) then α=

A+B=π4 then (1+tan⁡A)(1+tan⁡B)=2⇒α+4α=π4⇒5α=π4⇒α=π20

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If $(1 + \tan α) (1 + \tan 4 α) = 2, α \in (0, \frac{π}{16})$ then $α =$

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$\frac{π}{20}$

$\frac{π}{30}$

$\frac{π}{40}$

$\frac{π}{60}$

answer is A.

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Detailed Solution

$A + B = \frac{π}{4} then (1 + \tan A) (1 + \tan B) = 2$

$\Rightarrow α + 4 α = \frac{π}{4} \Rightarrow 5 α = \frac{π}{4} \Rightarrow α = \frac{π}{20}$

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If (1+tan⁡α)(1+tan⁡4α)=2,α∈(0,π16) then α=

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If $(1 + \tan α) (1 + \tan 4 α) = 2, α \in (0, \frac{π}{16})$ then $α =$