Ctg (pi/4-x) / (sinx+cosx) ^2

Представим в виде функции f (x) и преобразуем данное тригонометрическое выражение:

f (x) = ctg (π/4 - x) / (sinx + cosx) ^2; f (x) = cos (π/4 - x) / sin (π/4 - x) * 1 / (sinx + cosx) ^2; f (x) = (cos (π/4) * cosx + sin (π/4) * sinx) / (sin (π/4) * cosx - cos (π/4) * sinx) * 1 / (sinx + cosx) ^2; f (x) = (√2/2 * cosx + √2/2 * sinx) / (√2/2 * cosx - √2/2 * sinx) * 1 / (sinx + cosx) ^2; f (x) = (cosx + sinx) / (cosx - sinx) * 1 / (cosx + sinx) ^2; f (x) = 1 / (cosx - sinx) * 1 / (cosx + sinx); f (x) = 1 / (cos^2x - sin^2x); f (x) = 1/cos2x.

Ответ: 1/cos2x.