sin10*sin30*sin50*sin70 = sin[0,5(40-20)] * sin[0,5(40+20)] *sin[0,5(120-20)] * *sin[0,5(120+20)] = 0.5(cos20-cos40) * 0.5(cos20-cos120) = 0.25[(cos20)^2-cos40 * *cos20 - cos20 * cos120 +cos40 * cos120] = 0.25[(cos20)^2 - 0.5(cos20+cos60) + +0.5cos20 - 0.5cos40] = 0.25[(cos20)^2 - 0.5cos20 - 0.25 + 0.5cos20 - 0.5cos40] ==0.25[(cos20)^2 - 0.5cos40 - 0.25] =? (cos20)^2 = 0.5 + 0.5cos40 отсюда (cos20)^2 - 0.5cos40 =0.5Продолжим преобразования:0.25[(cos20)^2 - 0.5cos40 - 0.25] = 0.25[0.5 - 0.25] =0,25 * 0,25 =0,0625 =1/16ответ: 1/16 или 0,0625
sin10*sin30*sin50*sin70 = sin[0,5(40-20)] * sin[0,5(40+20)] *sin[0,5(120-20)] * *sin[0,5(120+20)] = 0.5(cos20-cos40) * 0.5(cos20-cos120) = 0.25[(cos20)^2-cos40 * *cos20 - cos20 * cos120 +cos40 * cos120] = 0.25[(cos20)^2 - 0.5(cos20+cos60) + +0.5cos20 - 0.5cos40] = 0.25[(cos20)^2 - 0.5cos20 - 0.25 + 0.5cos20 - 0.5cos40] =
=0.25[(cos20)^2 - 0.5cos40 - 0.25] =?
(cos20)^2 = 0.5 + 0.5cos40 отсюда (cos20)^2 - 0.5cos40 =0.5
Продолжим преобразования:
0.25[(cos20)^2 - 0.5cos40 - 0.25] = 0.25[0.5 - 0.25] =0,25 * 0,25 =0,0625 =1/16
ответ: 1/16 или 0,0625