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If sin4A-cos2A=cos4A-sin2A ("where",0l...

If `sin4A-cos2A=cos4A-sin2A` `("where",0ltAlt(pi)/(4))`, then the value of tan 4A is

A

1

B

`(1)/(sqrt(3))`

C

`sqrt(3)`

D

`(sqrt(3)-1)/(sqrt(3)+1)`

Text Solution

Verified by Experts

The correct Answer is:
C
`sin4A-cos4A=cos2A-sin2A`
On squaring both sides ,we get
1-2 sin 4 A cos 4 A = 1-2 sin 2 A cos 2 A
`rArrcos4A=(1)/(2)rArrtan4A=sqrt(3)`
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Knowledge Check

  • If sin 4 A - cos 2A = cos 4A - sin 2A, (0 lt A lt (pi)/(4)) then the value of tan 4A is

    A
    1
    B
    `(1)/(sqrt(3))`
    C
    `(sqrt(3))`
    D
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  • If si 4 A - cos 2A = cso 4A - sin 2A (0 lt A lt (pi)/(4)), then the value of tan 4A=

    A
    1
    B
    `(1)/(sqrt3)`
    C
    `sqrt3`
    D
    `(sqrt3-1)/(sqrt3+1)`

  • If int_(0)^(t) (bx cos 4x- a sin 4x)/(x^(2)) dx= (a sin 4t)/(t)-1 , where 0 lt t lt (pi)/(4) , then the value of a, b are equal to

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    `(1)/(4), 1`
    B
    `-1, 4`
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