Question

Докажите тоджество:

tgα / 1 - tg²α × ctg²α-1 / ctgα = 1

Answer 1

$\frac{tg(\alpha)}{1 - tg^2(\alpha)} * \frac{ctg^2(\alpha) - 1}{ctg(\alpha)} = 1$

$tg(\alpha) * ctg(\alpha) = 1$

$\frac{tg(\alpha)}{1 - tg^2(\alpha)} * \frac{ctg^2(\alpha) - 1}{ctg(\alpha)} = \frac{ctg(\alpha) - tg(\alpha)}{ctg(\alpha) - tg(\alpha)} = 1$