已知sina-cosa=1/5,0≤a≤π,求sin(2a-π/4)的值

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已知sina-cosa=1/5,0≤a≤π,求sin(2a-π/4)的值
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已知sina-cosa=1/5,0≤a≤π,求sin(2a-π/4)的值
已知sina-cosa=1/5,0≤a≤π,求sin(2a-π/4)的值

已知sina-cosa=1/5,0≤a≤π,求sin(2a-π/4)的值
(sin⁡a-cos⁡a)^2=1/25
sin^2a+cos^2a-2sinacosa=1/25
Sin^2a+cos^2a=1
sinacosa=12/25
消去sina或cosa可解二元一次方程求得:
(0≤a≤π)
Sina=4/5 cosa=3/5
Sin(2a-π/4)=√2/2(sin2a-cos2a)=31√2/50