найдите sin альфа-cos альфа, если tg альфа = -3/4 и пи/2 < альфа < пи

   1. Вычислим ctgα:

• tgα = -3/4;
• ctgα = 1/tgα = 1/(-3/4) = -4/3.

   2. Выразим функции sinα и cosα через tgα и ctgα, для α ∈ (π/2; π):

• sin^2(α) + cos^2(α) = 1;
• sin^2(α)/cos^2(α) + cos^2(α)/cos^2(α) = 1/cos^2(α);
• tg^2(α) + 1 = 1/cos^2(α);
• cos^2(α) = 1/(1 + tg^2(α));
• cosα = -1/√(1 + tg^2(α)) = -1/√(1 + 9/16) = -1/√(25/16) = -1/(5/4) = -4/5;

• sin^2(α) + cos^2(α) = 1;
• sin^2(α)/sin^2(α) + cos^2(α)/sin^2(α) = 1/sin^2(α);
• 1 + ctg^2(α) = 1/sin^2(α);
• sin^2(α) = 1/(1 + ctg^2(α));
• sinα = 1/√(1 + ctg^2(α)) = 1/√(1 + 16/9) = 1/√(25/9) = 1/(5/3) = 3/5.

   3. sinα - cosα = 3/5 - (-4/5) = 3/5 + 4/5 = 7/5 = 1,4.