sin2α=24∕25,0<α<π/2,则根号2cosα﹙π/4﹣α﹚=?

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sin2α=24∕25,0<α<π/2,则根号2cosα﹙π/4﹣α﹚=?
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sin2α=24∕25,0<α<π/2,则根号2cosα﹙π/4﹣α﹚=?
sin2α=24∕25,0<α<π/2,则根号2cosα﹙π/4﹣α﹚=?

sin2α=24∕25,0<α<π/2,则根号2cosα﹙π/4﹣α﹚=?
因为00,即sinα+cosα>0
(sinα+cosα)^2=1+2sinαcosα=1+sin2α=49/25
所以sinα+cosα=7/5
所以2cos﹙π/4﹣α﹚=2(cosπ/4cosα+sinπ/4sinα)=√2(sinα+cosα)=7√2/5