Question

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

Answer 1

`\cos(x) \cot ^(2) (x)`

Step-by-step explanation

The given expression is;

`\cot^(2) (x) \sec(x) - \cos(x)`

Change everything to

`\sin(x)`

and

`\cos(x)`

This implies that,

`( \cos^(2) (x) )/( \sin^(2) (x) ) * ( (1)/( \cos(x) ) )- \cos(x)`

Cancel the common factors,

`( \cos(x) )/( \sin^(2) (x) ) * ( (1)/(1) )- \cos(x)`

`( \cos(x) )/( \sin^(2) (x) )- \cos(x)`

`( \cos(x) - \sin ^(2) (x) \cos(x) )/( \sin^(2) (x) )`

`= ( \cos(x)(1 - \sin ^(2) (x) ) )/( \sin^(2) (x) )`

`= ( \cos(x)(\cos^(2) (x) ) )/( \sin^(2) (x) )`

`= \cos(x) \cot^(2) (x)`