求证：sin10°cos10°sin20°......sin80°cos80°=(3/256)^2

王守恩

求证：sin10°cos10°sin20°cos20°sin30°cos30°sin40°cos40°sin50°cos50°sin60°cos60°sin70°cos70°sin80°cos80°=(3/256)^2

angel_phoenix88

原题=(cos10cos20cos30cos40sin40sin30sin20sin10)^2
=(sin20sin40sin80)^2*((sqrt(3)/(2^5))^2(1)

sin20sin40sin80=sin20sin40cos10=((sin20)^2)sin40/(2sin10)
=(1-cos40)sin40/(4sin10)=(sin(10+30)-sin80/2)/(4sin10)=sqrt(3)/8(2)
(1)(2)联立，需要求解的结果=(3/256)^2