設函數f(x)=1-1/2cos(2x)+asin(x/2)*cos(x/2)(a∈R)的最大值為3,試求a

設函數f(x)=1-1/2cos(2x)+asin(x/2)*cos(x/2)(a∈R)的最大值為3,試求a

f(x)=1-1/2cos(2x)+asin(x/2)*cos(x/2)
f(x)=(sinx)^2+(a/2)*sinx+1/2
sinx∈[-1,1]
對稱軸為-a/4
(1)-a/4>0
a