已知f(x)=2sin^2x-(cosx-sinx)^2

显示全部楼层 · 2013-2-20 20:41:48

f(x)=2sin^2x-(cosx-sinx)^2=2sin^2x-(cos^2x+sin^2x-2sinxcosx)=2sin^2x-1+2sinxcosx=-(1-2sin^2x)+2sinxcosx=-cos2x+sin2x=sin2x-cos2x=√2(√2/2sin2x-√2/2cos2x)=√2(sin2xcosπ/4-cos2xsinπ/4)=√2sin(2x-π/4)T=2π/2=π2x-π/4=2kπ+π/22x=2kπ+3π/4x=kπ+3π/8当x=kπ+3π/8时 f(x)取得最大值，最大值是:√22x-π/4∈(2kπ+π/2,2kπ+3π/2)2x∈(2k...

千问 · 2013-2-20 20:41:48

先化简f(x)=2sin^2x-cos^2x-sin^2x+2cosxsinx
=根号2cos(2x+4\π)周期T=2π\w=πx=kπ-π\8（k∈z）x∈[k-π\8,k+π\8]（k∈z）化简的时候用倍角公式和...