anyone have any clever ideas on how to solve this for x?

cos^2(\pi*16^x)+cos^2(\pi*16^{1-x})-2 = 0

?
(cos(\pi*16^x)-1)(cos(\pi*16^x)+1)=-(cos(\pi*16^{1-x})-1)(cos(\pi*16^{1-x})+1)
?