#LHS=(sec8alpha-1)/(sec4alpha-1)#
#=(1/(cos8alpha)-1)/(1/(cos4alpha)-1)#
#=((1-cos8alpha)/(cos8alpha))/((1-cos4alpha)/(cos4alpha))#
#=(2sin^2 4alphacos4alpha)/(2sin^2 2 alphacos8alpha)#
#=(sin 8alpha*sin4alpha)/(2sin^2 2 alphacos8alpha)#
#=(sin 8alpha*2sin2alphacos2alpha)/(2sin^2 2 alphacos8alpha)#
#=(tan 8alpha)/((sin 2 alpha)/(cos 2alpha)#
#=(tan 8alpha)/(tan 2 alpha)=RHS#