已知函数f(x)=cos^4x-2sinxcosx - 知识问答

已知函数f(x)=cos^4x-2sinxcosx-sin^4x.(1)求f(x)最小正周期;(2)当x属于[0,pai

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原式=(cos^2x+sin^2x)(cos^2x-sin^2x)-2sinxcosx
=cos^2x-sin^2x-2sinxcosx
=cos2x-sin2x
=√2[(√2/2)cos2x-(√2/2)sin2x]
=√2cos(π/4+2x)
周期2π/2=π
当π/4+2x=π+2kπ时,即x=3π/8+kπ时,f(x)最小=-√2

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