y=cosx(cosx+sinx)和y=cos2x-8cosx的值域

(1) y=cos²x+sinxcosx
=(1+cos2x)/2+(sin2x)/2
=(1/2)sin2x+(1/2)cos2x+1/2
=√2/2sin(2x+π/4)+1/2
值域 [1/2-√2/2,1/2+√2/2]
(2)y=2cos²x-1-8cosx
=2(cosx-2)²-9
cosx=1时,y有最小值-7
cosx=-1时,y有最大值9
值域[-7,9]