如何将y=(sin^2(x/4)+cos^2(x/4))^2-2sin^2(x/4)cos^2(x/4)变形到(3/4)+(1/4)cosx?
问题描述:
如何将y=(sin^2(x/4)+cos^2(x/4))^2-2sin^2(x/4)cos^2(x/4)变形到(3/4)+(1/4)cosx?
答
y=((1-cosx/2)/2+(1+cosx/2)/2)^2-2((1-cosx/2)/2)((1+cosx/2)/2)=(1)^2-1/2 * (1-cosx/2)(1+cosx/2)=1-1/2 * (1-cos^2(x/2))=1-1/2+1/2 * (1+cosx)/2=1/2+1/4+(1/4)cosx=3/4+(1/4)cosx