SOLUTION: If {{{ sin(x) + cos(x) = 1/2 }}}, compute {{{ sin(x)cos(x) }}} . (You may work on both sides.)

Square both sides of your equation. You will get

 = ,

 = ,


 = ,

2*sin(x)*cos(x) = ,  

sin(x)*cos(x) =                

Square both sides of the equation





Use FOIL on the left



The two middle terms are like terms, so they combine:



Swap the 2nd and 3rd term on the left



Recall the Pythagorean identity 



Clear the fraction by multiplying through by 4



Subtract 4 from both sides



Divide both sides by 8



Edwin