设函数f(x)=2sinxcos^2θ/2+cosxsinθ-sinx在△ABC中,a,b,c分别是角A,B,C的对边,已知a=1,b=根号2,f(A)=根号3/2,求角C

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设函数f(x)=2sinxcos^2θ/2+cosxsinθ-sinx在△ABC中,a,b,c分别是角A,B,C的对边,已知a=1,b=根号2,f(A)=根号3/2,求角C

设函数f(x)=2sinxcos^2θ/2+cosxsinθ-sinx在△ABC中,a,b,c分别是角A,B,C的对边,已知a=1,b=根号2,f(A)=根号3/2,求角C
设函数f(x)=2sinxcos^2θ/2+cosxsinθ-sinx
在△ABC中,a,b,c分别是角A,B,C的对边,已知a=1,b=根号2,f(A)=根号3/2,求角C

设函数f(x)=2sinxcos^2θ/2+cosxsinθ-sinx在△ABC中,a,b,c分别是角A,B,C的对边,已知a=1,b=根号2,f(A)=根号3/2,求角C
f(A)=2sinAcos^2θ/2+cosAsinθ-sinA
=sinA(1+cosθ)+cosAsinθ-sinA
=sin(A+θ) 即f(x)=sin(x+θ)
=√3/2
A+θ=π/3或2π/3
正弦定理:a/sinA=b/sinB=c/sinC
余弦定理:cosC = (a^2 + b^2 - c^2) / (2·a·b)
cosB = (a^2 + c^2 -b^2) / (2·a·c)
cosA = (c^2 + b^2 - a^2) / (2·b·c)
三角形内角和:A+B+C=π
是否漏了条件?

f(A)=2sinAcos^2θ/2+cosAsinθ-sinA
=sinA(1+cosθ)+cosAsinθ-sinA
=sin(A+θ)=√3/2