Question 1051343
<font color=black size=3>
We'll use a <a href = "http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf">trig identity</a>. Specifically, we'll use this trig identity:


{{{sin(A) - sin(B) = 2*cos((A+B)/2)*sin((A-B)/2)}}}


where in this case, {{{A = pi/4}}} and {{{B = pi/6}}}



Note: see page 2 under the "Sum to Product Formulas" section



-----------------------------------------------------------------------------------------------------------------------------



{{{sin(A) - sin(B) = 2*cos((A+B)/2)*sin((A-B)/2)}}}



{{{sin(pi/4) - sin(pi/6) = 2*cos((pi/4+pi/6)/2)*sin((pi/4-pi/6)/2)}}} Plug in {{{A = pi/4}}} and {{{B = pi/6}}}



{{{sin(pi/4) - sin(pi/6) = 2*cos((3pi/12+2pi/12)/2)*sin((3pi/12-2pi/12)/2)}}} 



{{{sin(pi/4) - sin(pi/6) = 2*cos((5pi/12)/2)*sin((pi/12)/2)}}} 



{{{sin(pi/4) - sin(pi/6) = 2*cos((5pi/12)*(1/2))*sin((pi/12)*(1/2))}}} 



{{{sin(pi/4) - sin(pi/6) = 2*cos(5pi/24)*sin(pi/24)}}} 



---------------------------------------------------------------------------------------------------------------------------



The final answer is {{{2*cos(5pi/24)*sin(pi/24)}}}
</font>