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???

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

(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.