若2sin(π/4+a)=sinθ+cosθ,2sin^2β=sin2θ,求证sin2a+(1/2)cos2β=0

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若2sin(π/4+a)=sinθ+cosθ,2sin^2β=sin2θ,求证sin2a+(1/2)cos2β=0

若2sin(π/4+a)=sinθ+cosθ,2sin^2β=sin2θ,求证sin2a+(1/2)cos2β=0
若2sin(π/4+a)=sinθ+cosθ,2sin^2β=sin2θ,求证sin2a+(1/2)cos2β=0

若2sin(π/4+a)=sinθ+cosθ,2sin^2β=sin2θ,求证sin2a+(1/2)cos2β=0
2sin(π/4+α)=√2(sina+cosa)
√2(sina+cosa)=sinθ+cosθ 将这个式子平方,得
2(1+sin2a)=1+sin2θ 2sin2β=sin2θ
2(1+sin2a)=1+2sin2β
2+2sin2a=1+2sin2β
sin2α+1=2sin2β
所以
(sin2α+1)/2sin2β=1

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