作业帮已知函数f(x)=2sin的平方（π/4+x)减去根号下3cos2x-1,x∈R,若在x∈[π/4,π/2]上恒成立,不等式f(x)＞m的已知函数f(x)=2sin^2(π/4+x)-根号3cos2x-1,x∈R,若在x∈[π/4,π/2]上恒成立,不等式f(x)>m的平方减去3m+3恒
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![已知函数f(x)=2sin的平方（π/4+x)减去根号下3cos2x-1,x∈R,若在x∈[π/4,π/2]上恒成立,不等式f(x)＞m的已知函数f(x)=2sin^2(π/4+x)-根号3cos2x-1,x∈R,若在x∈[π/4,π/2]上恒成立,不等式f(x)>m的平方减去3m+3恒](/uploads/image/z/2687179-67-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2sin%E7%9A%84%E5%B9%B3%E6%96%B9%EF%BC%88%CF%80%2F4%2Bx%29%E5%87%8F%E5%8E%BB%E6%A0%B9%E5%8F%B7%E4%B8%8B3cos2x-1%2Cx%E2%88%88R%2C%E8%8B%A5%E5%9C%A8x%E2%88%88%5B%CF%80%2F4%2C%CF%80%2F2%5D%E4%B8%8A%E6%81%92%E6%88%90%E7%AB%8B%2C%E4%B8%8D%E7%AD%89%E5%BC%8Ff%28x%29%EF%BC%9Em%E7%9A%84%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2sin%5E2%28%CF%80%2F4%2Bx%29-%E6%A0%B9%E5%8F%B73cos2x-1%2Cx%E2%88%88R%2C%E8%8B%A5%E5%9C%A8x%E2%88%88%5B%CF%80%2F4%2C%CF%80%2F2%5D%E4%B8%8A%E6%81%92%E6%88%90%E7%AB%8B%2C%E4%B8%8D%E7%AD%89%E5%BC%8Ff%28x%29%3Em%E7%9A%84%E5%B9%B3%E6%96%B9%E5%87%8F%E5%8E%BB3m%2B3%E6%81%92)
已知函数f(x)=2sin的平方（π/4+x)减去根号下3cos2x-1,x∈R,若在x∈[π/4,π/2]上恒成立,不等式f(x)＞m的已知函数f(x)=2sin^2(π/4+x)-根号3cos2x-1,x∈R,若在x∈[π/4,π/2]上恒成立,不等式f(x)>m的平方减去3m+3恒
已知函数f(x)=2sin的平方（π/4+x)减去根号下3cos2x-1,x∈R,若在x∈[π/4,π/2]上恒成立,不等式f(x)＞m的
已知函数f(x)=2sin^2(π/4+x)-根号3cos2x-1,x∈R,若在x∈[π/4,π/2]上恒成立,不等式f(x)>m的平方减去3m+3恒成立,求实数m的取值范围?请帮帮忙明天就要用了谢谢!
已知函数f(x)=2sin的平方（π/4+x)减去根号下3cos2x-1,x∈R,若在x∈[π/4,π/2]上恒成立,不等式f(x)＞m的已知函数f(x)=2sin^2(π/4+x)-根号3cos2x-1,x∈R,若在x∈[π/4,π/2]上恒成立,不等式f(x)>m的平方减去3m+3恒
f(x)=2sin²(π/4+x)- √3cos2x-1
=1-cos(π/2+2x)-√3cos2x-1
=sin2x-√3cos2x
=2sin(2x-π/3),
π/4≤x≤π/2,π/6 ≤2x-π/3≤2π/3,1/2 ≤sin(2x-π/3)≤1
1≤ f(x)≤2,
f(x)＞m²-3m+3恒成立,就是1>m²-3m+3恒成立,
1
你的题目没有说清楚。。
f(x)=2sin²(π/4+x)- √3cos2x-1
=1-cos(π/2+2x)-√3cos2x-1
=sin2x-√3cos2x
=2sin(2x-π/3),
π/4≤x≤π/2, π/6 ≤2x-π/3≤2π/3, 1/2 ≤sin(2x-π/3)≤1
1≤ f(x)≤2,
f(x)＞m²-3m+3恒成立，就是1>m²-3m+3恒成立，
1