Question

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)

Answer 1

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