函数y=[(1+sinx+cosx)/(1+sinx-cosx)]+[(1+sinx+cosx)/(1+sinx-cosx)]最小正周期

cos2p=2cos^2p-1=1-2sin^2p
设x=2p,p=x/2
1+sinx+cosx=1+2sinp*cosp+2cos^2p-1=2cosp*(sinp+cosp)
1+sinx-cosx=1+2sinp*cosp-(1-2sin^2p)=2sinp*(sinp+cosp)
[(1+sinx+cosx)/(1+sinx-cosx)]=cosp/sinp
y=[(1+sinx+cosx)/(1+sinx-cosx)]+[(1+sinx+cosx)/(1+sinx-cosx)]
=2[(1+sinx+cosx)/(1+sinx-cosx)]
=2cosp/sinp
=2ctanp
=2ctan(x/2)
到这里你应该懂了哦