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Grade: 12

                        

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

5 years ago

Answers : (1)

AUREA
61 Points
							
     (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  ; )
5 years ago
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