The Rate of Change of the Function $f ( x ) = - \csc x - \sin x$

Multiple Choice

The rate of change of the function $f ( x ) = - \csc x - \sin x$ is given by the expression $\csc x \cot x - \cos x$ . Which of the following is its simplification?

A) $- \csc x \sec ^ { 2 } x$
B) $\tan ^ { 2 } x \cos x$
C) $\cot ^ { 2 } x \cos x$
D) $- \cot x \cos ^ { 2 } x$
E) $\sec ^ { 2 } x$