If (1+ tan A)(1+ tan 4A)= 2, A E ( 0, π/16), THEN A is equal to


(a) π/20  (b) π/30   (c) π/40  (d) π/60


 Explain how???

2 years ago

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Answers : (2)

                    

let A +B = pi/4 


tan(A+B)=1


or, tanA +tanB = 1-tanAtanB


or, (1+tanA)(1+tanB)=2




 use this result to obtain A+4A = pi/4


 


A= pi/20

2 years ago
                    

(1+tanA)(1+tan4A)=2,


1+tanA+tan4A+tanAtan4A=2,


tanA+tan4A+tanAtan4A=1,


tanA+tan4A=1-tanAtan4A,


(tanA+tan4A)/(1-tanAtan4A)=1,


tan(A+4A)=tan45,


tan5A=tan45,


thus 5A=45,


A=9.


then (a) is the ans.

2 years ago

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