If (1+tanalpha)(1+tan4alpha)=2,alpha in ...

If `(1+tanalpha)(1+tan4alpha)=2,alpha in (0,pi/(16)),` then `alpha` is equal to (a)`pi/(20)` (b) `pi/(30)` (c) `pi/(40)` (d) `pi/(60)`

A

`(pi)/(20)`

B

`(pi)/(30)`

C

`(pi)/(40)`

D

`(pi)/(60)`

Verified by Experts

`(1+tanA)(1+tanB)=2`
`rArr tan A+tan B=1-tan A tan B`
`rARr tan(A+B)=1,i.e, A+B=(pi)/(4)`
or `alpha+4alpha=(pi)/(4)` i.e. `alpha=(pi)/(20)`

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