Question 1083298
(1) sin(x)*cos(x)<pre>Given: {{{sin(x)+cos(x)=1/2}}}

Square both sides:

{{{sin^2(x)+ 2sin(x)cos(x)+ cos^2(x)=1/4}}}

{{{sin^2(x)+ cos^2(x) + 2sin(x)cos(x)=1/4}}}

{{{(sin^2(x)+ cos^2(x)^"") + 2sin(x)cos(x)=1/4}}}

{{{1+2sin(x)cos(x)=1/4}}}

{{{2sin(x)cos(x)=-3/4}}}

{{{sin(x)cos(x)=-3/8}}}

---------------</pre>(2) sin^2(x)+cos^2(x)<pre>That's just 1.

-----------------------------------</pre>(3) sin^3(x)+cos^3(x)<pre>
Factor as the sum of two cubes:

{{{(sin(x)^""+cos(x)^"")(sin^2(x)^""-sin(x)cos(x)+cos^2(x))}}}

Plug in the values from above parts:

{{{(1/2)(1-(-3/8)^"")}}}

{{{(1/2)(1+3/8)}}}

{{{(1/2)(11/8)}}}

{{{11/16}}}

Edwin</pre>