```                   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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```                    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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