已知:sin(π/4+α)sin(π/4-α)=1/6,且α∈(π/2,π),求sin2α
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已知:sin(π/4+α)sin(π/4-α)=1/6,且α∈(π/2,π),求sin2α
已知:sin(π/4+α)sin(π/4-α)=1/6,且α∈(π/2,π),求sin2α
已知:sin(π/4+α)sin(π/4-α)=1/6,且α∈(π/2,π),求sin2α
sin(π/4+α)sin(π/4-α)
=√2/2(sina+cosa)*√2/2(cosa-sina)
=1/2(cos^2 a-sin^2 a)
=1/2cos2a=1/6
cos2a=1/3
α∈(π/2,π),2α∈(π,2π),
sin2a=-2√2/3
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