求函数y=2cos^2+2sinx cosx-1,(x属于R)的值域

问题描述:

求函数y=2cos^2+2sinx cosx-1,(x属于R)的值域

y=2(1+cos2x)/2+sin2x-1
=sin2x+cos2x
=√2(√2/2*sin2x+√2/2*cos2x)
=√2(sin2xcosπ/4+cos2xsinπ/4)
=√2sin(2x+π/4)
-1