Here is the Question -
By Assuming solutions of the from E=Eocos(kz-wt) and B=Bocos(kz-wt), show that Maxwells eqns lead to transverse EM waves, so that E.B=0 and there is no component of the fields in the direction of propagation.

These seemed fairly straight forward but I just cant work it out. Visually its easy to see but I cant get the proof to work. Any help would be appreciated.

I AM FINDING SOMETHING USING CURL OF E =-del B/delt
the Z component of Left side is vanishing. so the right side must.
and the components when compared is giving a hint of an underlying crossproduct.
please wait! i am working on it.