Question 1027158

Prove the identity csc x- cos x cot x = sin x
<pre>{{{csc (x) - cos (x) cot (x) = highlight(sin (x))}}}
The left side will be proven to be equal to the right side
{{{1/sin (x) - cos (x) * (cos (x)/sin (x))}}} ------- Replacing {{{matrix(1,3, csc (x), with, 1/sin (x))}}}, and {{{matrix(1,3, cot (x), with, cos (x)/sin (x))}}}  
{{{1/sin (x) - cos^2 (x)/sin (x)}}}
{{{(1 - cos^2 (x))/sin (x)}}} 
{{{sin^2 (x)/sin (x)}}} ------- Replacing {{{matrix(1,3, 1 - cos^2 (x), with, sin^2 (x))}}}
{{{(sin (x) * sin (x))/sin (x)}}} = {{{(sin (x) * cross(sin (x)))/cross(sin (x))}}} = {{{highlight_green(sin (x))}}}
{{{highlight_green(sin (x)) = highlight(sin (x))}}} (PROVEN)