sin²10°＋sin²50°＋sin10°sin50°=

sin²10°＋sin²50°＋sin10°sin50°=
sin²10°＋sin²50°＋sin10°sin50°=

sin²10°＋sin²50°＋sin10°sin50°=
用到公式cos2a=1-2sin^2 a　sinαsinβ=-[cos（α+β）-cos（α-β）] /2 cosθ+cosφ=2cos[（θ+φ）/2]cos[（θ-φ）/2]
原式=1/2-1/2cos20 +1/2-1/2cos100 -1/2 cos60+1/2cos(-40)
=3/4-1/2(cos20+cos100-cos40)
=3/4-1/2(cos20-cos80-cos40)
=3/4-1/2(cos20-2cos60cos20)
=3/4

sin²10°＋sin²50°＋sin10°sin50°= sin²10°＋sin²50°-2sin10°sin50°coc120°
=sin²120°=sin²60=3/4