it is given that e^jwt=cos(wt)+jsin(wt)...
but j=1 with angle 90 degrees..now by multiplying any function by j means multiplying the magnitude by 1 and phase change of 90 degree...
so,
jsin(wt)=sin(wt)*1 with angle 90 degrees
= sin(wt+90)
=cos(wt)...