Tgα+2tg2α+4tg4α+8tg8a+16tg16a+32ctg32α=ctgα;
tgα+2tg2α+4tg4α+8tg8α+(16tg16α+32ctg32α)=
=tgα+2tg2α+4tg4α+8tg8α+(16tg16α+32·(1-tg²16α)/2tg16α)=
=tgα+2tg2α+4tg4α+8tg8α+(32tg²16α+32-32tg²16α)/2tg16α=
=tgα+2g2α+4tg4α+(8tg8α+16ctg16α)=
=tgα+2tg2α+4tg4α+(16tg²8α+16-16tg²8α)/2tg8α=
=tgα+2tg2α+(4tg4α+8ctg8α)=
=tgα+(2tg2α+4ctg4α)=tgα+2ctg2a=(2tg²α+2-2tg²α)/2tgα=2/2tgα=ctgα;
ctgα=ctgα;