f(x)=cos^2x+2sinxcosx+3si - 知识问答

f(x)=cos^2x+2sinxcosx+3sin^x求最值

2个回答

f(x)=cos^2x+2sinxcosx+3sin^2x
=(cos^2x+sin^2x)+2sinxcosx+2sin^2x
=1+2sinxcosx+2sin^2x
=1+sin2x+1-cos2x
=2+(sin2x-cos2x)
=2+√2(√2/2sin2x-√2/2cos2x)
=2+√2sin(x+π/4)
所以：
当x=2kπ+π/4时,函数有最大值＝2+√2
当x=2kπ-3π/4时,函数有最小值＝2-√2

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