Question 704213
<pre>
             {{{1- expr(1/2)sin(2theta)}}}{{{""=""}}}{{{(sin^3(theta) + cos^3(theta))/(sin(theta)+cos(theta))}}}

Factor the numerator on the right side as the sum of 
two cubes, using {{{A^3+B^3}}}{{{""=""}}}{{{(A+B)(A^2-AB+B^2)}}}

                    {{{""=""}}}{{{
((sin(theta)+cos(theta))(sin^2(theta)-sin(theta)cos(theta)+cos^2(theta)))/

(sin(theta)+cos(theta))}}}

                   {{{""=""}}}{{{
((cross(sin(theta)+cos(theta)))(sin^2(theta)-sin(theta)cos(theta)+cos^2(theta)))/

(cross(sin(theta)+cos(theta)))}}}

                   {{{""=""}}}{{{sin^2(theta)-sin(theta)cos(theta)+cos^2(theta)}}}

Use the identity {{{sin^2(alpha)+cos^2(alpha)=1}}} on the 1st and 3rd terms:

                   {{{""=""}}}{{{1-sin(theta)cos(theta)}}}

Use the identity {{{sin(2alpha)=2sin(alpha)cos(alpha)}}} multiplied
through by {{{1/2}}} or {{{expr(1/2)sin(2alpha)=sin(alpha)cos(alpha)}}}

                   {{{""=""}}}{{{1-sin(theta)cos(theta)}}}

                   {{{""=""}}}{{{1- expr(1/2)sin(2theta)}}}

Edwin</pre>