设f(x)=sin^2 x+asin^2 (x/2),求f(x)最大值

f(x)=sin^2 x+asin^2 (x/2)
=sin^2 x+a(1-cosx)
=1-cos^2 x +a-acosx 1
=-(cos^2 x +acosx)+a+1
=-(cos^2 x +acosx +a^2/4) +a+1+a^2/4
=-(cosx+a/2)^2 +(a^2+4a+4)/4
=-(cosx+a/2)^2+(a+2)^2/4
当-1

f(x)=1-cos²x+a*(1-cosx)/2=-cos²x-a/2*cosx+(1+a)=-(cosx+a/4)²+(a²/16+a+1)
设cosx=t，则-1<=t<=1,，f(t)=-(t+a/4)²+（a²/16+a+1)
对称轴t=-a/4
(1)若-a/4>=1，即a<=-4时，t=1，f(x)最...