已知函数f(x)=cos^2x+sinxcosx

f(x)=cos^2x+(1/2)sin2x.
f(x)=(1+cos2x)/2+(1/2)sin2x .
=(1/2)(sin2x+cos2x)+1/2.
∴f(x)=(1/2)√2sin(2x+π/4)+1/2.
若sinα=3/5,α∈(π/2,π),则 f(α/2+π/24)=?
f(α/2+π/24)=(√2/2)sin[2(α/2+π/24)]+1/2.
=(√2/2)sin(α+π/12)+1/2.
=(√2/2)[sinαcos(π/12)+cosαsin(π/12)]+1/2.
[sin(π/12=√2/4(√3-1),cos(π/12)=√2/4(√3+1)]+1/2
原式=(√2/2)[(3/5)(√2/4)*(√3+1)+(-4/5)(√2/4)(√3-1)]+1/2
∴原式=19/20-√3/20.