化简:根号3 sin(2x+pai/3)+ 2sin^2(x+pai/6)

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化简:根号3 sin(2x+pai/3)+ 2sin^2(x+pai/6)

化简:根号3 sin(2x+pai/3)+ 2sin^2(x+pai/6)
化简:根号3 sin(2x+pai/3)+ 2sin^2(x+pai/6)

化简:根号3 sin(2x+pai/3)+ 2sin^2(x+pai/6)
根号3 sin(2x+pai/3)+ 2sin^2(x+pai/6)
=根号3 sin(2x+pai/3)+ 2-2cos^2(x+pai/6)
=根号3 sin(2x+pai/3)-cos(2x+pai/3)+ 1
=2sin(2x+pai/3-pai/6)+ 1
=2sin(2x+pai/6)+ 1

根号3 Sin(2x+pai/3)+ 2Sin^2(x+pai/6)
=根号3Sin(2x+Pai/3)-[1-2Sin^2(x+Pai/6)]+1
=根号3Sin(2x+Pai/3)-Cos(2x+Pai/3)+1
=2[根号3/2Sin(2x+Pai/3)-1/2Cos(2x+Pai/3)]+1
=2Sin(2x+Pai/6)+1


原式=√3*sin(2x+π/3)+1-cos(2x+π/3)
=1+2*[sin(2x+π/3)*(√3/2)-cos(2x+π/3)*(1/2)]
=1+2[sin(2x+π/3)*cosπ/6-cos(2x+π/3)*sinπ/6]
=1+2sin(2x+π/3-π/6)
=1+2sin(2x+π/6)