Известно. что ctg(3пи/2 + t)=4/5 и пи/2<t<пи найдите: а) tg(3пи/2-t) б) tg(3пи +t) d)...

$ctg (\frac{3 \pi}{2}+t) = \frac{4}{5}$
$-tg t = \frac{4}{5}$
$tg t = -\frac{4}{5}$
$ctg t = -\frac{5}{4}$

a). $tg ( \frac{3 \pi}{2}-t) = ctg t = -\frac{5}{4}$
б). $tg ( 3 \pi + t) = tg t = -\frac{4}{5}$
в). $sin ( \frac{\pi}{2}+t) = cos t = -\sqrt{\frac{1}{1+tg^{2}t}} =-\sqrt{\frac{1}{1+\frac{16}{25}}} =-\sqrt{\frac{25}{41}} = -\frac{5}{\sqrt{41}}= -\frac{5\sqrt{41}}{41}$