Ответ:

Дано: ctg(A) = -2. Найти: Cos(2A).

ctg^2(A) = 4

tg^2(A) = 1/4

1). tg^2(A)+1=1/Cos^2(A)

5/4=1/Cos^2(A)

Cos^2(A) = 4/5

2). ctg^2(A)+1=1/Sin^2(A)

5 = 1/Sin^2(A)

Sin^2(A) = 1/5

3). Cos(2A) = Cos^2(A) - Sin^2(A)

Cos^2(A) - Sin^2(A) = 4/5 - 1/5 = 3/5

Ответ: Cos(2A) = 3/5 или 0,6