已知tana=2,求sina.sin(a-π/4)

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已知tana=2,求sina.sin(a-π/4)
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已知tana=2,求sina.sin(a-π/4)
已知tana=2,求sina.sin(a-π/4)

已知tana=2,求sina.sin(a-π/4)
tan(a-π/4) =(tana-1)/(tana+1) =(2-1)/(2+1) =1/3.sin^2a+sinacosa-2cos^2a =(sina+2cosa)(sina-cosa) =(2cosa+2cosa)(2cosa-

sina=2√5/5 sin(a-π/4)=sinacosπ/4-cosasinπ/4=2√5/5*√2/2-√5/5*√2/2=3√10/10