函数y=cos^2x-2sinxcosx-sin^2x的值域是多少

问题描述:

函数y=cos^2x-2sinxcosx-sin^2x的值域是多少

y=cos^2x-2sinxcosx-sin^2x
=cos2x-sin2x
=√2(sinπ/4cos2x-cosπ/4sin2x)
=√2(-2x+π/4)
所以:函数y=cos^2x-2sinxcosx-sin^2x的值域是[-√2,√2]