Question 105526
(sin x + cos x)^2
Using the FOIL Method, 
{{{(sin x + cos x)^2=sin^2(x)+2cos(x)sin(x)+cos^2(x)}}} FOIL method. 
You know the following trig identity,
{{{sin^2(x)+cos^2(x)=1}}}
Substitute that in your equation,
{{{(sin x + cos x)^2=1+2cos(x)sin(x)}}}
Another indentity (fundamental identity, I think) is,
{{{sin(2x)=2sin(x)cos(x)}}}
Substitute that into your equation, 
{{{(sin x + cos x)^2=1+2cos(x)sin(x)}}}
{{{(sin x + cos x)^2=1+sin(2x)}}}