Given:

Let y=2 cos x cos 3x

So y=cos 2x+cos 4x

=(-2)¹ (sin 2x+2¹ sin 4x )

=(-2)² (cos 2x+2² cos 4x )

=(-2)³ (cos 2x+2³ cos 4x )

=(-2)⁴ (cos 2x+2⁴ cos 4x )

For every odd degree; differential = =(-2)ⁿ (cos 2x+2ⁿ cos 4x );n={1,3,5…}

For every even degree; differential =(-2)ⁿ (cos 2x+2ⁿ cos 4x );n={0,2,4…}

So,

=(-2)²⁰ (cos 2x+2²⁰ cos 4x );