求证 cos(A)+ 根号3sin(A)=2sin(π/6+A)

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求证 cos(A)+ 根号3sin(A)=2sin(π/6+A)

求证 cos(A)+ 根号3sin(A)=2sin(π/6+A)
求证 cos(A)+ 根号3sin(A)=2sin(π/6+A)

求证 cos(A)+ 根号3sin(A)=2sin(π/6+A)
右边2sin(π/6+A)=2sin(π/6)cosA+2sinAcos(π/6)=cosA+根号3sin(A)=左式.得证#

左边=2(√3/2*sinA+1/2*cosA)
=2(sinAcosπ/6+cosAsinπ/6)
=2sin(A+π/6)=右边

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