Question

Упростить выражение :

Answer 1

(ctg (9π/2 + α) · cos(α - 5π))/(ctg(3π - α) · cos(7π/2 - α)) + tg (5π + α) =

(-tg α · (-cos α))/(-ctg α · (-cos α)) + tg α =

= tg α / ctg α + tg α = tg α (1 + 1/ctg α) = tg α (1 + tg α)

Answer 2

$a = \frac{ctg(\frac92\pi+x)cos(x-5\pi)}{ctg(3\pi-x)cos(\frac72\pi - x)} + tg(5\pi+x)\\ctg(\frac92\pi+x) = ctg(4\pi + \frac\pi2 + x) = ctg(\frac\pi2+x) = -tgx\\cos(x - 5\pi) = cos(-4\pi - \pi +x) = cos(-\pi +x) = -cosx\\ctg(3\pi - x) = ctg(2\pi+\pi-x) = ctg(\pi-x) = -ctgx\\cos(\frac72\pi-x) = cos(2\pi + \frac32\pi -x) = cos(\frac32\pi -x) = -sinx\\tg(5\pi +x) = tg(4\pi+ \pi+x) = tg(\pi+x) = -tgx\\a = \frac{tgx*cosx}{ctgx*sinx} - tgx = \frac{sinx}{cosx}-tgx = tgx-tgx = 0$