Доказать тождество [latex]tg \alpha + 2tg2 \alpha + 4tg4 \alpha + 8tg8 \alpha + 16tg16 \alpha + 32ctg32 \alpha = ctg \alpha [/latex]

Решение смотри в приложении

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;