Упростите выражение: (cos)^2 α +(sin(π/2+α)*cos(π-α)/(ctg(π-α)*tg(3π/2-α))

   1. Формулы приведения тригонометрических функций:

• sin(π/2 + α) = cosα;
• cos(π - α) = -cosα;
• ctg(π - α) = - ctgα;
• tg(3π/2 - α) = tg(π + π/2 - α) = tg(π/2 - α) = ctgα.

   2. Преобразуем заданное выражение:

• f(α) = cos^2(α) + (sin(π/2 + α) * cos(π - α))/(ctg(π - α) * tg(3π/2 - α));
• f(α) = cos^2(α) + (cosα * (-cosα))/(-ctgα * ctgα);
• f(α) = cos^2(α) + (-cos^2(α))/(-ctg^2(α));
• f(α) = cos^2(α) + cos^2(α) * tg^2(α);
• f(α) = cos^2(α) + cos^2(α) * sin^2(α)/cos^2(α);
• f(α) = cos^2(α) + sin^2(α);
• f(α) = 1;

   Ответ: 1.