函数y=cosx-sinx+2sinxcosx的值域是

问题描述:

函数y=cosx-sinx+2sinxcosx的值域是

y=cosx-sinx+2sinxcosx=cosx-sinx+(sinx+cosx)²-1=√2cos(x+π/4)+2sin²(x+π/4)-1
=-2cos²(x+π/4)+√2cos(x+π/4)+1=-2[cos(x+π/4)-√2/4]²+5/4
y∈[-1-√2,5/4];