题目没写完,是否要求a的值.
f(π/2)=(2cosπ/2+asinπ/2)sinπ/2+cos^2(π/2)
=(0+a)*1+0=a
f(π/4)=(2cosπ/4+asinπ/4)sinπ/4+cos^2(π/4)
=(根号2+a*二分之根号2）*二分之根号2+
二分之一 = 1+ (1/2)a +1/2 =3/2+(1/2)a
所以 a=3/2+(1/2)a,所以 a=3
f(x)=(2cosx+3sinx)sinx+cos^2 x=2cosxsinx+2sin^2x+1
f(x)=sin2x+2(1-cos2x)/2+1
f(x)=sin2x-cos2x+2=根号2sin(2x-π/4)+2