cosX*sin(X+1)的值域?

cosxsin(x+1)=sin(x+0.5+0.5)cos(x+0.5-0.5)
=[sin(x+0.5+0.5+x+0.5-0.5)+sin(x+0.5+0.5-x-0.5+0.5)]/2
=[sin(2x+1)+sin1]/2
值域就是[(-1+sin1)/2,(1+sin1)/2]

f(x)=cosx*sin(x+1)=cosx(sinxcos1+cosxsin1)=cosxsinxcos1+cos^2xsin1
=1/2cos1sin2x+sin1(cos2x+1)/2=cos1sin2x/2+sin1cos2x/2+sin1/2
=√[((cos1)^2+(sin1)^2)/4]sin(2x+φ)+sin1/2
(用到公式asinx+bcosx=√(a^2+b^2)sin(x+φ))
=1/2sin(2x+φ)+sin1/2
-1≤sin(2x+φ)≤1
-1/2+1/2*sin1≤f(x)≤1/2+1/2*sin1
值域为[-1/2+1/2*sin1,1/2+1/2*sin1]