已知sin(π-α)=4/5,α∈(0,π/2) (1)求sin2α-cos^2(α/2)的值(1)求sin2α-cos^2(α/2)的值(2)求函数f(x)=5/6cosαsin2x-1/2cos2x的单调递增区间
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![已知sin(π-α)=4/5,α∈(0,π/2) (1)求sin2α-cos^2(α/2)的值(1)求sin2α-cos^2(α/2)的值(2)求函数f(x)=5/6cosαsin2x-1/2cos2x的单调递增区间](/uploads/image/z/657625-49-5.jpg?t=%E5%B7%B2%E7%9F%A5sin%28%CF%80-%CE%B1%29%3D4%2F5%2C%CE%B1%E2%88%88%280%2C%CF%80%2F2%29+%EF%BC%881%EF%BC%89%E6%B1%82sin2%CE%B1-cos%5E2%EF%BC%88%CE%B1%2F2%EF%BC%89%E7%9A%84%E5%80%BC%281%29%E6%B1%82sin2%CE%B1-cos%5E2%EF%BC%88%CE%B1%2F2%EF%BC%89%E7%9A%84%E5%80%BC%282%29%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%3D5%2F6cos%CE%B1sin2x-1%2F2cos2x%E7%9A%84%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4)
已知sin(π-α)=4/5,α∈(0,π/2) (1)求sin2α-cos^2(α/2)的值(1)求sin2α-cos^2(α/2)的值(2)求函数f(x)=5/6cosαsin2x-1/2cos2x的单调递增区间
已知sin(π-α)=4/5,α∈(0,π/2) (1)求sin2α-cos^2(α/2)的值
(1)求sin2α-cos^2(α/2)的值
(2)求函数f(x)=5/6cosαsin2x-1/2cos2x的单调递增区间
已知sin(π-α)=4/5,α∈(0,π/2) (1)求sin2α-cos^2(α/2)的值(1)求sin2α-cos^2(α/2)的值(2)求函数f(x)=5/6cosαsin2x-1/2cos2x的单调递增区间
已知sin(π-α)=4/5,α∈(0,π/2)
∴根据诱导公式得,sinα=4/5,又α∈(0,π/2),∴cosα=3/5
(1)sin2α-cos²(α/2)=2sinαcosα-(1+cosα)/2=8/5;
(2)f(x)= 5/6cosαsin2x-1/2cos2x
=1/2sin2x-1/2cos2x
=(√2/2)sin(2x-π/4)
∵α∈(0,π/2),∴2x-π/4∈(-π/4,3π/4)
当2x-π/4∈(-π/4,0)即x∈(0,π/8)时,f(x)为增函数,
∴f(x)的单调递增区间为(0,π/8).
1,由sin(π-α)=4/5,且α∈(0,π/2)得sina=4/5;cosa=3/5;sin2α-cos^2(α/2)=2sinacosa-(1+cosa)/2=4/25;
2,f(x)=根号2/2(sin(2x-π/4)),增区间为(-π/8+kπ,3π/8+kπ),k是整数