求f(a)=(2cos^3-sin(a+π)-2cos(-a-π)+1)/(2+2cos^2(7π+a)+cosa 求f(π/3)的值?

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求f(a)=(2cos^3-sin(a+π)-2cos(-a-π)+1)/(2+2cos^2(7π+a)+cosa 求f(π/3)的值?

f(a)={2cos^3a-sin(a+π)-2cos(-a-π)+1}/(2+2cos^2(7π+a)+cosa ={2cos^3a+sina-2cos(a+π)+1}/{(2+2cos^2(π+a)+cosa }=={2cos^3a+sina+2cosa+1}/{2+2cos^2a+cosa }
当a=π/3
f(π/3)={2cos^3(π/3)+sin(π/3)+2cos(π/3)+1}/{2+2cos^2(π/3)+cos(π/3) }
={2(1/2)^3+√3/2+2×1/2+1}/{2+2(1/2)^2+(1/2) }
=(1/4+√3/2+2)/3=(9+2√3)/12