若cos2α/sin(α-π/4)=-√2/2,则cosα+sinα的值为?

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若cos2α/sin(α-π/4)=-√2/2,则cosα+sinα的值为?

cos2α/sin(α-π/4)=-√2/2
(cos^2α-sin^2α)/(sinαcosπ/4-cosαsinπ/4) = -√2/2
[(cosα+sinα)(cosα-sinα)] / [√2/2(sinα-cosα)] = -√2/2
-√2(cosα+sinα)(cosα-sinα) / (cosα-sinα) = -√2/2
-√2(cosα+sinα) = -√2/2
cosα+sinα = 1/2