1+cosx=?,1-cosx=?公式不是很熟啊,我只知道,1-cos2x=2sin^2x.1+cos2x=2cos^2x.然后书上那题突然来个1+cosx=2-2sin^2(x/2)1-cosx=2-2cos^2(x/2)怎么变出来的啊,求详细变形经过啊.

Question

1+cosx=?,1-cosx=?
公式不是很熟啊,我只知道,1-cos2x=2sin^2x.1+cos2x=2cos^2x.然后书上那题突然来个 1+cosx=2-2sin^2(x/2) 1-cosx=2-2cos^2(x/2)怎么变出来的啊,求详细变形经过啊.

Answer 1

1+cos2x=2cos^2x
1+cosx=2cos^2(x/2)=2(1-sin^2(x/2)=2-2sin^2(x/2)
1-cos2x=2sin^2x
1-cosx=2sin^2(x/2)=2(1-cos^2(x/2)=2-2cos^2(x/2)