Question 959308
if CosA+SinA=1, show that CosA-SinA=±1
<pre>
{{{cos(A)+sin(A)=1}}}, which is given:

Square both sides:

{{{cos^2(A)+2cos(A)sin(A)+sin^2(A)=1}}}

{{{(cos^2(A)^""+sin^2(A))+(2sin(A)cos(A)^"")=1}}}

{{{1 + sin(2A)=1}}}

{{{sin(2A)=0}}}

{{{2A = n*pi}}}
 
{{{A = n*expr(pi/2)}}}

If n is even, {{{sin(A)=0}}} and {{{cos(A)= "" +- 1}}}, then {{{cos(A)-sin(A)= "" +- 1}}}

If n is odd,  {{{sin(A)= "" +- 1}}} and {{{cos(A)=0}}}, then {{{cos(A)-sin(A)= "" +- 1}}}

Edwin</pre>