y=cos2x+sinxcosx的值域y=cos^2X+sinXcosX

y=cos2x+sinxcosx的值域y=cos^2X+sinXcosX
y=cos2x+sinxcosx的值域
y=cos^2X+sinXcosX

y=cos2x+sinxcosx的值域y=cos^2X+sinXcosX
y=cos²X-1/2+sinXcosX +1/2
=1/2(2cos²x-1 + 2sinxcosx) +1/2
=1/2(cos2x+sin2x)+1/2
=1/2[√2(√2/2cos2x+√2/2sin2x)]+1/2
=1/2[√2sin(π/4+2x)]+1/2
=√2/2sin(π/4+2x)+1/2
最大(√2+1)/2 最小(1-√2)/2
值域[(1-√2)/2,(√2+1)/2]

y=cos^2x+sinxcosx
=(1+cos2x)/2+1/2*sin2x
=1/2*cos2x+1/2*sin2x+1/2
=√2/2*(√2/2*cos2x+√2/2*sin2x)+1/2
=√2/2*(sinπ/4cos2x+cosπ/4sin2x)+1/2
=√2/2*sin(π/4+2x)+1/2
-1<=sin(π/4+2x)<=1
-√2/2<=√2/2sin(π/4+2x)<=√2/2
所以-√2/2+1/2<=y<=√2/2+1/2

y=cos^2X+sinXcosX
=(Cos2x)/2 +1/2 + (Sin2x)/2
=(√2/2) × Sin(2x +π/4) ＋1/2
因为，|Sin(2x +π/4)|<=1
所以，(1-√2)/2<=y<=(1+√2)/2
所以，y的值域为[(1-√2)/2，(1+√2)/2]