Question

Докажите тоджество:

tgα / 1 - tg²α × ctg²α-1 / ctgα = 1

Answer 1

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

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

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