Question 69789
Use identity
{{{sin(u-v)=sin(u)cos(v)-cos(u)sin(v)}}}
Let {{{u=pi/3}}} and {{{v=pi/4}}}
{{{sin(pi/3-pi/4)=sin(pi/3)cos(pi/4)-cos(pi/3)sin(pi/4)}}}
Using the unit circle, {{{sin(pi/4)=cos(pi/4)=sqrt(2)/2}}} and {{{sin(pi/3)=sqrt(3)/2}}}, and {{{cos(pi/3)=1/2}}}
{{{sin(pi/3-pi/4)=(sqrt(3)/2)*(sqrt(2)/2)-(1/2)*(sqrt(2)/2)}}}
{{{sin(pi/3-pi/4)=sqrt(6)/4-sqrt(2)/4}}}
{{{sin(pi/3-pi/4)=(sqrt(6)-sqrt(2))/4}}}