Question 1137318


{{{sin(4pi/9)cos(pi/9) - cos(4pi/9)sin(pi/9) }}}


Use the following identity :

{{{sin (s)cos (t)-cos (s)sin (t)=sin (s-t) }}}


in your case {{{s=4pi/9 }}}and {{{t=pi/9}}}


{{{sin(4pi/9)cos(pi/9) - cos(4pi/9)sin(pi/9) =sin (4pi/9 -pi/9 ) }}}


{{{sin(4pi/9)cos(pi/9) - cos(4pi/9)sin(pi/9) =sin (3pi/9  ) }}}


{{{sin(4pi/9)cos(pi/9) - cos(4pi/9)sin(pi/9) =sin (pi/3  ) }}}



Use the following  identity : {{{sin  ( pi/3 )= sqrt(3)/2}}}


{{{sin(4pi/9)cos(pi/9) - cos(4pi/9)sin(pi/9) =sqrt(3)/2}}}