已知函数f(x)=根号3sin^2x+sinxcosx-根号3/2
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已知函数f(x)=根号3sin^2x+sinxcosx-根号3/2
()若f(阿法)=4/5,且阿法属于(0,派/2),求cos2阿法的值()在ABC中,若A
()若f(阿法)=4/5,且阿法属于(0,派/2),求cos2阿法的值()在ABC中,若A
f(x)=√3sin^2x+sinxcosx-√3/2
=-√3/2*cos2x+1/2*sin2x
=sin(2x-π/3),
f(α)=sin(2α-π/3)=4/5,
α∈(0,π/2),
2α-π/3∈(-π/3,2π/3),
∴cos(2α-π/3)=土3/5,
∴cos2α=cos(2α-π/3+π/3)=土3/5*1/2-4/5*√3/2=(土3-4√3)/10.
A
=-√3/2*cos2x+1/2*sin2x
=sin(2x-π/3),
f(α)=sin(2α-π/3)=4/5,
α∈(0,π/2),
2α-π/3∈(-π/3,2π/3),
∴cos(2α-π/3)=土3/5,
∴cos2α=cos(2α-π/3+π/3)=土3/5*1/2-4/5*√3/2=(土3-4√3)/10.
A
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