Question 985310
<pre>
{{{(1^""-sin(A)^""+cos(A))^2}}}  {{{"?=?"}}}  {{{2(1-sin(A)^"")^""(1+cos(A)^"")}}}

Square out the left side:

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

Replace sinē(A) by 1-cosē(A):

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

Remove parentheses:

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

Combine like terms:

{{{2-2sin(A)+2cos(A)-2sin(A)cos(A)}}}

Factor out 2:

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

Factor by grouping:  I.e., In the parentheses factor 1 out 
of the first two terms and factor cos(A) out of the last 
two terms:

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

Factor 1-sin(A) out of both terms:

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

Edwin</pre>