已知sin(a-π/4)=7根号2/10,cos2a=7/25,求sina及tan(a+π/3)

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已知sin(a-π/4)=7根号2/10,cos2a=7/25,求sina及tan(a+π/3)

已知sin(a-π/4)=7根号2/10,cos2a=7/25,求sina及tan(a+π/3)
已知sin(a-π/4)=7根号2/10,cos2a=7/25,求sina及tan(a+π/3)

已知sin(a-π/4)=7根号2/10,cos2a=7/25,求sina及tan(a+π/3)
sin(α-45°)=√2/2(sinα-cosα)=7√2/10
→sinα-cosα=7/5
cos2α=cosα^2-sinα^2=7/25
→sinα=3/5,cosα=-4/5
tan(α+60°)=(tanα+tan60°)/(1-tanα*tan60°)=(-3/4+√3)/(1+3/4*√3)
=(48-25√3)/11