By comparing the multiple ,
how do you find k for
l 1- exp (ix) l = k l sin ( x/2) l for all real x
i tried to square both sides of the equation and i got:
1- ( cos (^2) x + sin(^2) x ) -2i sin x( 1- cos x) -2 cos x = k^2 sin(^ 2) ( x/2)
factorising the sin (^2) ( x/2) terms to one side,
sin (^2) (x/2) ( 4 - 4 i sin x) -2 = k(^2) sin(^2) ( x/2)
and then i got stuck..