Question 985645
{{{highlight_green(cot(-x) * cos(-x) + sin(-x) = -csc(x))}}}


Necessary to understand  {{{cos(-x)=cos(x)}}} and {{{sin(-x)=-sin(x)}}}.
If unsure how, check on the unit circle.


L.H.S., {{{(cos(-x)/sin(-x))cos(-x)+sin(-x)}}}
{{{(cos(x)/(-sin(x)))cos(x)+(-sin(x))}}}
{{{-(cos^2(x)/sin(x)+sin(x))}}}
{{{-((cos^2(x)+sin^2(x))/(sin(x)))}}}
{{{-(1/sin(x))}}}
and by definition
{{{-csc(x)}}}