ENG: For the best approximations of en-1(ƒ) functions from C12π by trigonometric polynomials, Zhuk earlier proved the exact Jackson inequality en-1(ƒ),,π/4n*ɷ(ƒ',π/n). This paper proves the following version of Jackson's exact inequality: en-1(ƒ),,π/4n*﴾(1/2ɷ(ƒ',π/2n)+1/2ɷ(ƒ',π/n)﴿.