已知函数f(x)=(1+cotx)sin^2(x)-2sin(x+π/4)sin(x-π/4)
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已知函数f(x)=(1+cotx)sin^2(x)-2sin(x+π/4)sin(x-π/4)
1,若tana=2,求f(a)
2,若x∈【π/12,π/2】,求f(x)的取值范围.
1,若tana=2,求f(a)
2,若x∈【π/12,π/2】,求f(x)的取值范围.
公式忘了,就凑乎着做吧
1.(1+cotx)sin^2(x)-2sin(x+π/4)sin(x-π/4)=(1+cosx/sinx)sin^2(x)-(cosπ/2-cos2x)
=sin^2(x)+cosxsinx-+cos2x=cosxsinx+cos^2(x)=cos^2(x)(tanx+1)
f(a)=cos^2(a)(tana+1)=3*1/5=3/5
2.f(x)=cos^2(x))(tanx+1)=sinxcosx+cos^2(x))=1/2sin2x+1/2(cos2x)+1/2
=1/2+根号2/2sin(2x+π/4)
π/12=<x<π/2,π/6=<2x<=π,5/12π=<2x+π/4<=5/4π
2x+π/4=5/4π时 sin(2x+π/4)=-根号2/2(最小
2x+π/4=π/2时 sin(2x+π/4)=-1最大
所以 0=< f(x)==1/2+根号2/2sin(2x+π/4)<=(1+根号2)/2
f(x)∈[0,(1+根号2)/2]
1.(1+cotx)sin^2(x)-2sin(x+π/4)sin(x-π/4)=(1+cosx/sinx)sin^2(x)-(cosπ/2-cos2x)
=sin^2(x)+cosxsinx-+cos2x=cosxsinx+cos^2(x)=cos^2(x)(tanx+1)
f(a)=cos^2(a)(tana+1)=3*1/5=3/5
2.f(x)=cos^2(x))(tanx+1)=sinxcosx+cos^2(x))=1/2sin2x+1/2(cos2x)+1/2
=1/2+根号2/2sin(2x+π/4)
π/12=<x<π/2,π/6=<2x<=π,5/12π=<2x+π/4<=5/4π
2x+π/4=5/4π时 sin(2x+π/4)=-根号2/2(最小
2x+π/4=π/2时 sin(2x+π/4)=-1最大
所以 0=< f(x)==1/2+根号2/2sin(2x+π/4)<=(1+根号2)/2
f(x)∈[0,(1+根号2)/2]
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