Доказательство:

Разделим обе части равенства на sin(a):

tg(a)/sin(a) + ctg(a)/sin(a) = 2/sin(2a)

tg(a) = sin(a)/cos(a), ctg(a) = cos(a)/sin(a)

(sin(a)/cos(a))/sin(a) + (cos(a)/sin(a))/sin(a) = 2/sin(2a)

(cos(a)/cos(a)) + (sin(a)/sin(a)) = 2/sin(2a)

1 + 1 = 2/sin(2a)

2 = 2/sin(2a)

Таким образом, тождество tg(a) + ctg(a) = 2/sin(2a) доказано.