ANSWER
[tex] \cos(x) \cot ^{2} (x) [/tex]
EXPLANATION
The given expression is;
[tex] \cot^{2} (x) \sec(x) - \cos(x) [/tex]
Change everything to
[tex] \sin(x) [/tex]
and
[tex] \cos(x) [/tex]
This implies that,
[tex] \frac{ \cos^{2} (x) }{ \sin^{2} (x) } \times ( \frac{1}{ \cos(x) } )- \cos(x) [/tex]
Cancel the common factors,
[tex] \frac{ \cos(x) }{ \sin^{2} (x) } \times ( \frac{1}{1} )- \cos(x) [/tex]
[tex] \frac{ \cos(x) }{ \sin^{2} (x) }- \cos(x) [/tex]
[tex] \frac{ \cos(x) - \sin ^{2} (x) \cos(x) }{ \sin^{2} (x) } [/tex]
[tex] = \frac{ \cos(x)(1 - \sin ^{2} (x) ) }{ \sin^{2} (x) } [/tex]
[tex] = \frac{ \cos(x)(\cos^{2} (x) ) }{ \sin^{2} (x) } [/tex]
[tex] = \cos(x) \cot^{2} (x) [/tex]
