已知f(x)=2sin²x+2sinx*cosx-1 (x∈R)(1)求函数f(x)周期和单调递减区间(2)若f(A/2+π/8)=3√2/5,且A∈(π/2,π) 求cos2A和tan2A的值
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![已知f(x)=2sin²x+2sinx*cosx-1 (x∈R)(1)求函数f(x)周期和单调递减区间(2)若f(A/2+π/8)=3√2/5,且A∈(π/2,π) 求cos2A和tan2A的值](/uploads/image/z/8659204-52-4.jpg?t=%E5%B7%B2%E7%9F%A5f%EF%BC%88x%EF%BC%89%3D2sin%26%23178%3Bx%2B2sinx%2Acosx-1+%EF%BC%88x%E2%88%88R%EF%BC%89%EF%BC%881%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E5%91%A8%E6%9C%9F%E5%92%8C%E5%8D%95%E8%B0%83%E9%80%92%E5%87%8F%E5%8C%BA%E9%97%B4%EF%BC%882%EF%BC%89%E8%8B%A5f%EF%BC%88A%2F2%2B%CF%80%2F8%EF%BC%89%3D3%E2%88%9A2%2F5%2C%E4%B8%94A%E2%88%88%EF%BC%88%CF%80%2F2%2C%CF%80%EF%BC%89+%E6%B1%82cos2A%E5%92%8Ctan2A%E7%9A%84%E5%80%BC)
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已知f(x)=2sin²x+2sinx*cosx-1 (x∈R)(1)求函数f(x)周期和单调递减区间(2)若f(A/2+π/8)=3√2/5,且A∈(π/2,π) 求cos2A和tan2A的值
已知f(x)=2sin²x+2sinx*cosx-1 (x∈R)
(1)求函数f(x)周期和单调递减区间
(2)若f(A/2+π/8)=3√2/5,且A∈(π/2,π) 求cos2A和tan2A的值
已知f(x)=2sin²x+2sinx*cosx-1 (x∈R)(1)求函数f(x)周期和单调递减区间(2)若f(A/2+π/8)=3√2/5,且A∈(π/2,π) 求cos2A和tan2A的值
f=2(sinx)^2+2sinxcosx
=1-cos2x+sin2x
=1+根号2((根号2/2)*sin2x-(根号2/2)*cos2x)
=1+根号2sin(2x-45)
最大值 1+根号2
周期T=2π/2=π
确定没抄错题