已知函数f(x)=4sin(x+π/6)cosx-1,求f(π/12)需要FX的化简即可.

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已知函数f(x)=4sin(x+π/6)cosx-1,求f(π/12)需要FX的化简即可.

已知函数f(x)=4sin(x+π/6)cosx-1,求f(π/12)需要FX的化简即可.
已知函数f(x)=4sin(x+π/6)cosx-1,求f(π/12)
需要FX的化简即可.

已知函数f(x)=4sin(x+π/6)cosx-1,求f(π/12)需要FX的化简即可.
f(x)=4sin(x+π/6)cosx-1
=4(sinxcosπ/6+cosxsinπ/6)cosx-1
=4(√3/2 sinx+1/2 cosx)cosx-1
=2√3sinxcosx+2cos^2 x-1
=√3*(2sinxcosx)+(2cos^2 x-1)
=√3sin2x+cos2x
=2(√3/2 sin2x+1/2cos2x)
=2(sin2xcosπ/6+cos2xsinπ/6)
=2sin(2x+π/6)
带入π/12
f(π/12) =2sin(2*π/12+π/6)=2sin(π/3)=2*√3/2=√3
和楼上结果一致,收工~