`(d^(20)y)/(dx^(20))(2cosxcos3x)is equal to ` `2^(20)(cos2x-2^(20)os3x)` `2^(20)(cos2x+2^(20)cos4x)` `2^(20)(sin2x+2^(20)sin4x)` `2^(20)(sin2x-2^(20)sin4x)`

Options

A. `2^(20)( cos 2x -2^(20) cos 3x)`
B. `2^(20)( cos 2x +2^(20) cos 4x)`
C. `2^(20)( sin 2x +2^(20) sin 4x)`
D. `2^(20)( sin 2x - 2^(20) sin 4x)`

Explanation

To solve the problem \(\frac{d^{20}}{dx^{20}}(2\cos x \cos 3x)\), we will use the trigonometric identity for the product of cosines.

### Step-by-Step Solution:

1. **Apply the Trigonometric Identity**:
We start with the identity:
\[
2 \cos a \cos b = \cos(a + b) + \cos(a - b)
...