函数f(x)=2倍根号3sinxcosx+2cos - 知识问答

函数f(x)=2倍根号3sinxcosx+2cos^2x-1若(x)=6/5,x0属于[兀/4.兀/2],求cos2xo

1个回答

f(x)=2倍根号3sinxcosx+2cos^2x-1
=√3sin2x+cos2x
=2sin(2x+π/6)
2sin(2x0+π/6)=6/5
sin(2x0+π/6)=3/5 cos(2x0+π/6)=-4/5
cos2xo=cos[(2x0+π/6)-π/6]
=cos(2x0+π/6)cosπ/6+sin(2x0+π/6)sinπ/6
=-4/5*√3/2+3/5*1/2
=(3-4√3)/10

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