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If sin 4 A - cos 2A = cos 4A - sin 2A, ...

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

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

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \( \sin 4A - \cos 2A = \cos 4A - \sin 2A \) for the value of \( \tan 4A \), we can follow these steps: ### Step 1: Rearranging the Equation Starting with the given equation: \[ \sin 4A - \cos 2A = \cos 4A - \sin 2A \] We can rearrange it to: \[ \sin 4A + \sin 2A = \cos 4A + \cos 2A \]
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Knowledge Check

  • 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
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    D
    `(sqrt3-1)/(sqrt3+1)`

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

    A
    1
    B
    `(1)/(sqrt(3))`
    C
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    D
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  • If (2 sin A + cosec A) = 2sqrt 2 , 0^@ lt A lt 90^@ , then the value of 2(sin^4 + cos^4A) is :

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    0
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    2
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