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已知函数Fx=2Cosxsin(x加三分之派)%根号三sin平...

f(x) = sin(π/2-x)sinx - √3cos²x = cosxsinx - √3cos²x = 1/2sin2x - √3/2cos2x - √3/2 = sin2xcosπ/3-cos2xsinπ/3 - √3/2 = sin(2x-π/3) - √3/2 最小正周期:2π/2 = π 最大值:1 - √3/2 = (2-√3)/2

f(x)=4cosxsinx-4sin(x +派/3)cosx +根号3 =2sin2x-4(1/2*sinx+根号3/2*cosx)cosx+根号3 =2sin2x-(2sin2x+2根号3cos平方x)+根号3 =根号3-2根号3cos平方x

f(x)=[2sin(x+π/3)+sinx]cosx-根号3sin^2x和差角公式展开f(x)=(sinx+根号3cosx+sinx)cosx-根号3sin2x=2sinx*cosx+根号3cosx*cosx-根号3sin2x降幂公式f(x)=sin2x+根号3*(1+cos2x)/2-根号3sin2x=(1-根号3)sin2x+根号3/2cos2x+根号3/2 辅助角公...

fx=2√3sinxcosx+2cos^2 x -1=√3sin2x+cos2x=2(√3/2 sin2x +1/2 cos2x)=2sin(2x+π/6)最小正周期 f(x)=根号3sin2x+cos2x =2(cosπ/6sin2x+sinπ/6cos2x) =2sin(2x+π/6)因为函数在区间[0,π/2]上所以π/6≤2x+π/6≤7π/6当2x+π/6=π/2,即x=π/6时...

f(x)=√3/2sin2x-(cosx)²-½ =√3/2sin2x-1/2cos2x-1 =sin(2x-π/6)-1 T=2π/2=π 2x-π/6在[2kπ+π/2,2kπ+3π/2]是调递减 x在[kπ+π/3,kπ+5π/6]是调递减

因为:函数f(x)=2cosx·sin(x+π/3)-√3(sinx)^2+sinx·cosx =2cosx·sin(x+∏/3)-√3(sinx)^2+sinx·cosx =2cosx·sinx·cos∏/3+2cosx·cosx·sin∏/3-√3(sinx)^2+sinx·cosx =cosx·sinx+√3(cosx)^2-√3(sinx)^2+sinx·cosx =2cosx·sinx+√3cos2x =sin2x+√3cos2...

解: 已知△ABC中,AB=AC,BD⊥AC,且BD=1/2AB 求∠BAC的度数 解:作BD⊥AC,交直线AC于点D (1)当点D在AC上时 ∵BD=1/2AB ∴∠BAC=30° (2)当点D在CA的延长线上时, ∵BD=1/2AB ∴∠BAD=30° ∴∠BAC=150° f'(x)=2x-m/x, h'(x)=2x-1, 取f'(x)=0,得m=2x^2;x=√m/2,...

解答: 换元,令t=cosx ∵ -π/4

f(x)=sin^2x+√3sinxcosx+2cos^2x =cos^2x+√3/2*2sinxcosx+1 =1/2cos2x+√3/2sin2x+3/2 =sinx(2x+π/6)+3/2 T=2π/2=π 2x+π/6在[2kπ-π/2,2kπ+π/2]上单调递增 x在[kπ-5π/12,kπ+π/6]上单调递增 2)y=sin2x的图像经X轴向左平移π/12个单位得到y=sinx(2x+...

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