Question 488109
{{{(1-(Sinx+Cosx)^2)/(2Sinx)}}}

{{{(1-(Sin^2x+2SinxCosx+Cos^2x))/(2Sinx)}}}

Get the Sin²x and the Cos²x together because we know an identity
for their sum:

{{{(1-(Sin^2x+Cos^2x+2SinxCosx))/(2Sinx)}}}

That identity is Sin²x + Cos²x = 1 so we have

{{{(1-(1+2SinxCosx))/(2Sinx)}}}

Then removing the parentheses on top:

{{{(1-1-2SinxCosx)/(2Sinx)}}}

{{{(-2SinxCosx)/(2Sinx)}}}

Cancel 2Sinx

{{{(-cross(2Sinx)Cosx)/(cross(2Sinx))}}}

{{{-Cosx}}}

Edwin</pre>