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

Options

A. 1
B. `(1)/(sqrt(3))`
C. `(sqrt(3))`
D. `(sqrt(3)-1)/(sqrt(3)+1)`

Answer

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:
\[ \sin 4A + \sin 2A = \cos 4A + \cos 2A \]