Question

Simplify the following expression. cot^2x secx-cosx

Answer 1

ANSWER

$\cos(x) \cot ^{2} (x)$

EXPLANATION

The given expression is;

$\cot^{2} (x) \sec(x) - \cos(x)$

Change everything to

$\sin(x)$

and

$\cos(x)$

This implies that,

$\frac{ \cos^{2} (x) }{ \sin^{2} (x) } \times ( \frac{1}{ \cos(x) } )- \cos(x)$

Cancel the common factors,

$\frac{ \cos(x) }{ \sin^{2} (x) } \times ( \frac{1}{1} )- \cos(x)$

$\frac{ \cos(x) }{ \sin^{2} (x) }- \cos(x)$

$\frac{ \cos(x) - \sin ^{2} (x) \cos(x) }{ \sin^{2} (x) }$

$= \frac{ \cos(x)(1 - \sin ^{2} (x) ) }{ \sin^{2} (x) }$

$= \frac{ \cos(x)(\cos^{2} (x) ) }{ \sin^{2} (x) }$

$= \cos(x) \cot^{2} (x)$