作业帮F(x)=[cos^3x-sin^2(x+pai)-cos(x+pai)+1]/[1+cos^2(7pai+x)+cos(-x),化简并求F（5pai/3）
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![F(x)=[cos^3x-sin^2(x+pai)-cos(x+pai)+1]/[1+cos^2(7pai+x)+cos(-x),化简并求F（5pai/3）](/uploads/image/z/13321725-69-5.jpg?t=F%28x%29%3D%5Bcos%5E3x-sin%5E2%28x%2Bpai%29-cos%28x%2Bpai%29%2B1%5D%2F%5B1%2Bcos%5E2%287pai%2Bx%29%2Bcos%28-x%29%2C%E5%8C%96%E7%AE%80%E5%B9%B6%E6%B1%82F%EF%BC%885pai%2F3%EF%BC%89)
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F(x)=[cos^3x-sin^2(x+pai)-cos(x+pai)+1]/[1+cos^2(7pai+x)+cos(-x),化简并求F（5pai/3）
F(x)=[cos^3x-sin^2(x+pai)-cos(x+pai)+1]/[1+cos^2(7pai+x)+cos(-x),化简并求F（5pai/3）
F(x)=[cos^3x-sin^2(x+pai)-cos(x+pai)+1]/[1+cos^2(7pai+x)+cos(-x),化简并求F（5pai/3）
f(x)=[(cosx)^3+1-(sinx)^2+cosx]/[1+(cosx)^2+cosx]
=[(cosx)^3+(cosx)^2+cosx]/[(cosx)^2+cosx+1]
=cosx[(cosx)^2+cosx+1]/[(cosx)^2+cosx+1]
=cosx
f(5π/3)=cos5π/3=cos(π+2π/3)=-cos2π/3=-(-1/2)=1/2