若sin2α=1/4,π/4

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若sin2α=1/4,π/4
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若sin2α=1/4,π/4
若sin2α=1/4,π/4

若sin2α=1/4,π/4
2*sin a*cos a=1/4;
(sin a)^2+(cos a)^2=1;
联立,解得.

(cosα-sinα)^2=cos^2α+sin^2-2sinαcosα=1-1/4=3/4因为π/4<α<π/2,所以cosα-sinα<0,所以cosα-sinα=-√3/2