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

$a = frac{ctg(frac92pi+x)cos(x-5pi)}{ctg(3pi-x)cos(frac72pi - x)} + tg(5pi+x)\ctg(frac92pi+x) = ctg(4pi + fracpi2 + x) = ctg(fracpi2+x) = -tgx\cos(x - 5pi) = cos(-4pi - pi +x) = cos(-pi +x) = -cosx\ctg(3pi - x) = ctg(2pi+pi-x) = ctg(pi-x) = -ctgx\cos(frac72pi-x) = cos(2pi + frac32pi -x) = cos(frac32pi -x) = -sinx\tg(5pi +x) = tg(4pi+ pi+x) = tg(pi+x) = -tgx\a = frac{tgx*cosx}{ctgx*sinx} - tgx = frac{sinx}{cosx}-tgx = tgx-tgx = 0$