cosπ/8=cos[(π/4)/2]
=√[1+cos(π/4)]/2
=√[1+(√2/2)]/2
=(1/2)√(2+√2)
cos(π/16)=cos[(π/6)/2]
=√[1+cos(π/8)]/2
=√{1+√[(2+√2)/4]}/2
=√{[4+√(2+√2)]/8}
cos(π/32)=cos[(π/16)/2]
=√[1+cos(π/16)]/2
=√{1+√[4+√(2+√2)]/8}/2
=(1/4)√{16+√[4+√(2+√2)}
sin(π/64)=sin[(π/32)/2]
=√[1-cos(π/32)]/2
=√{1-(1/4)√{16+√[4+√(2+√2)}}/2
=√{4-{16+√[4+√(2+√2)}}/8