已知函数f(x)=2cos(x/4+π/6),x∈R,设a,B∈[0,π/2],f(4a+4π/3)=-30/17,f(4B-2π/3)=8/5,求cos(a+B)的值

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已知函数f(x)=2cos(x/4+π/6),x∈R,设a,B∈[0,π/2],f(4a+4π/3)=-30/17,f(4B-2π/3)=8/5,求cos(a+B)的值
已知函数f(x)=2cos(x/4+π/6),x∈R,设a,B∈[0,π/2],f(4a+4π/3)=-30/17,f(4B-2π/3)=8/5,求cos(a+B)的值

已知函数f(x)=2cos(x/4+π/6),x∈R,设a,B∈[0,π/2],f(4a+4π/3)=-30/17,f(4B-2π/3)=8/5,求cos(a+B)的值

f(x)=2cos(x/4+π/6),
2cos[(4a+4π/3)/4+π/6]=-30/17 , cos[(a+π/2)=-15/17=-sina,sina=15/17,cosa=8/17
2cos[(4B-2π/3)/4+π/6]=8/5 , 2cosB=8/5 , cosB=4/5 ,sinB=3/5
cos(a+B)=(8/17)(4/5)-(15/17)(3/5)=-13/85