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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???

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???

Grade:12th Pass

2 Answers

aditya bhutra
18 Points
9 years ago

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

G Narayana Raju
51 Points
9 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.

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