sinα^2+sin(120°-α)^2怎么化简

题目

sinα^2+sin(120°-α)^2怎么化简

答案

sinα^2+sin(120°-α)^2=sinα^2+sin(60°+α)^2=sinα^2+[sin60cosα+cos60sinα]^2=sinα^2+(3/4cosα^2+1/4sinα^2+2*sin60*cos60*sinα*cosα)=1/2sinα^2+(3/4cosα^2+3/4sinα^2)+sin60sinαcosα=1/4（1-cos...