Determine Which of the Following Are Trigonometric Identities $\frac { \cos ( 4 x ) + \cos ( 2 x ) } { 2 \cot ( 3 x ) } = \cot ( x )$

Determine which of the following are trigonometric identities.
I. $\frac { \cos ( 4 x ) + \cos ( 2 x ) } { 2 \cot ( 3 x ) } = \cot ( x )$
II. $\frac { \cos ( 4 x ) + \cos ( x ) } { \sin ( 3 x ) - \sin ( x ) } = \cot ( 2 x )$
III. $\frac { \cos ( 6 x ) + \cos ( 2 x ) } { \sin ( 4 x ) + \sin ( 2 x ) } = \cot ( 3 x )$

A) III is the only identity.
B) I, II, and III are identities.
C) I is the only identity.
D) None are identities.
E) II is the only identity.