若((cos2a)/(sin(a+(π/4))))=-√2/2则cosa-sina的值是

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若((cos2a)/(sin(a+(π/4))))=-√2/2则cosa-sina的值是
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若((cos2a)/(sin(a+(π/4))))=-√2/2则cosa-sina的值是
若((cos2a)/(sin(a+(π/4))))=-√2/2则cosa-sina的值是

若((cos2a)/(sin(a+(π/4))))=-√2/2则cosa-sina的值是
由cos2α/sin(α-π/4)=-(√2)/2,

cos2α=cos²α-sin²α
sin(α-π/4)=(√2)/2*(sinα-cosα)
则:
cos2α/sin(α-π/4)=cos²α-sin²α/((√2)/2*(sinα-cosα))=-(√2)/2
等式左边同时约去sinα-cosα,可得:
√2(sinα+cosα)=-(√2)/2
则有:sinα+cosα=-1/2