求f(x)=sin²x+cosx+3的值域

分类讨论就别担心不对了①:当sinx-cosx>0:f(x)=1/2(sin+cosx-sinx+cosx)=cosx→-1≤f(x)≤1②当sinx-cosx

∵f（x）＝cos（2x－π/3）＋（sinx）^2－（cosx）^2＝cos（2x－π/3）－cos2x＝2sin（2x－π/6）sin（π/6）＝sin（2x－π/6）.∴g（x）＝［sin（2x

f(x)=[1+cos2x)/2]/[1+(1-cos2x)/2]=(1+cos2x)/(3-cos2x)=-1+4/(3-cos2x)f'(x)=-4/(2-cos2x)^2*(2-cos2x)'=

f'(sin^2x)=cos^2x=1-sin^2x所以f'(x)=1-x所以f(x)=∫(1-x)dx=x-x^2/2+C

f(x)=sin²(x)+(√3)sin(x)cos(x)+2cos²(x)=3/2+√3/2sin2x+1/2cos2x=3/2+sin(2x+π/6)函数f(x)的最小正周期T

f(x)=2sinx-3cosx=√13sin(x-φ）其中tanφ=3/2,sinφ=3/√13即φ=arcsin3/√13因0

f(x)=2sin(x/4)cos(x/4)+(√3)cos(x/2)=sin(x/2)+(√3)cos(x/2)=2sin(x/2+π/3)T=4π最大值2最小值-2（2）令g(x)=f(x+π/3

f(x)*f(y)的导数是f(x)的导数乘以f(y)+f(x)乘以f(y)的导数所以f(x)的导数是1-(1/2*cos(x/2)*cos(x/2)+sin(x/2)*(-sin(x/2))*1/2)

f(sin(pai/2-x))=cos[3(pai/2-x)]f(cosx)=cos(3pai/2-3x)f(cospai/9)=cos(3pai/2-pai/3)=-sinpai/3=-根号3/2f

f(x)=cos(3x)*cos(2x)+sin(3x)*sin(2x)=cos(3x-2x)=cosxf'(x)=-sinx

cosx=1-2(sinx/2)^2f=[sin(2/x)]=1+cosx=2-2(sinx/2)^2f(x)=2-2x^2f[cos(2/x)]=2-2[cos(2/x)]^2

设t=sinx,又cos2x=1-2(sinx)^2则f(t)=1-2(sinx)^2+1=2（1-t^2）所以f(cosx)=2（1-t^2）=2（1-(cosx)^2）=2(sinx)^2

f(3sinx)=cos方x/sin方x=（1-sin方x）/sin方x=1/sin方x-1=9/（3sinx)方-1f(x)=9/x^2-1

f'(x)=cos^2x则f(x)=∫cos^2xdx=x/2+sin2x/4+c;f(sin^2x)=sin^2x/2+sin2(sin^2x)/4+C

f(x)=cos^6x+sin^6x=(cos^2x+sin^2x)(cos^4x-sin^2xcos^2x+sin^4x)=cos^4x-sin^2xcos^2x+sin^4x=cos^4x+2si

f（x）=sin^2x+2√3sinxcosx+3cos^2x=1+√3sin2x+2cos^2x-1+1=√3sin2x+cos2x+2=2(sin2x*√3/2+cos2x*1/2)+2=2sin

也不知道你是f(sin(x/2))还是f((sinx)/2)?如果是第一种,利用半角公式：后面的看图,第二种不想做了.

f'(sin^2x)=cos^2x=1-sin^2x,利用X整体替换sin^2x,（0≤x≤1)得f'(x)=1-x所以原函数f(x)=x-(1/2)x^2+C,（0≤x≤1),其中C为任意常数.楼上

sinx=2cosx,sin^2x=4cos^2xsin^2x=4-4sin^2x,sin^2x=4/5(cosx+sinx)/(cosx-sinx)+sin^2x=(1+tanx)/(1-tanx)

f(x)=[cos(x)+sin(x)]sin(x)=cos(x)sin(x)+sin^2(x)=1/2sin2x+1/2(1-cos2x)=√2/2[cos(p/4)sin2x-sin(p/4)co