中科新闻网lpc1788教程:一道数学题
来源：百度文库 编辑：中科新闻网 时间：2024/04/29 22:13:59
已知f(x)=cos^4 x-2sinxcosx-sin^4 x,(1)求f(x)的最小正周期(2)若0<=x<=3.14/2,求f(X)的最大值,最小值.
f(x) = (cosx)^4 - 2sinx*cosx - (sinx)^4
= [(cosx)^2 + (sinx)^2] * [(cosx)^2 - (sinx)^2] - 2sinx*cosx
= cos(2x) + sin(2x)
= √2*[sin(2x + π/4)]
周期是 π
f(x) = (cosx)^4 - 2sinx*cosx - (sinx)^4
= [(cosx)^2 + (sinx)^2] * [(cosx)^2 - (sinx)^2] - 2sinx*cosx
= cos(2x) + sin(2x)
= √2*[sin(2x + π/4)]