cos²(x-π/4)-cos²(x+π/4)的取值范围

cos²(x-π/4)-cos²(x+π/4)的取值范围
cos²(x-π/4)-cos²(x+π/4)的取值范围

cos²(x-π/4)-cos²(x+π/4)的取值范围
原式=（cosxcosπ/4+sinxsinπ/4）^2-（cosxcosπ/4-sinxsinπ/4）^2
=1/2(1+sin2x)-1/2(1-sin2x)
=sin2x
如果x没有范围的话,那么原式的取值范围就是[-1,1]

解:
cos^2(x-π/4)-cos^(x+π/4)
=cos^2(x+π/4-π/2)+cos^(x+π/4)
=sin^2(x+π/4)+cos^2(x+π/4)
=1-cos^2(x+π/4)+cos^2(x+π/4)
=1

答：
cos²(x-π/4)-cos²(x+π/4)
=[cos(x-π/4)+cos(x+π/4)]*[cos(x-π/4)-cos(x+π/4)]
=2cosxcos(π/4)*2sinxsin(π/4)
=sin(2x)sin(π/2)
=sin(2x)∈[-1,1]
所以：取值范围为[-1,1]

=[cos(x-π/4)+cos(x+π/4)][cos(x-π/4)-cos(x+π/4)]
=[2cosx*cos(-π/4)][2sinx*sin(-π/4)]
= 4 cosx sinx * (-1/2) = -sin2x
所以取值范围[-1,1]