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

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

Grade:12

1 Answers

AUREA
61 Points
6 years ago
     (1+tan a)(1+tan 4a)=2
i.e  (1+sina/cosa)(1+sin4a/cos4a)=2
i.e  (sina+cosa)(sin4a+cos4a)/cosa cos4a=2
i.e  (cosa)(sin4a)+(sina)(cos4a)+(sina)(sin4a)+(cosa)(cos4a)=2(cosa)(cos4a)
i.e  sin(a+4a)=cos(a+4a)
i.e tan(a+4a)=1
i.e  tan 5a=1
i.e  5a=pi/4
i.e   a=pi/20
therefore a=pi/20
approve if useful  ; )

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