若cos2α/sin（α-π/4）=-√2/2，则cosα+sinα的值为？
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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
(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
追问
sinαcosπ/4-cosαsinπ/4，请教一下！
追答
sin（α-π/4）
= (sinαcosπ/4-cosαsinπ/4)
= (sinα*√2/2-cosα*√2/2)
= √2/2(sinα-cosα)
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