sinα=2sin（α+π/4）则tan(α+π/8)=

2sin(α+π/4) = 2[ sinαcosπ/4 + cosαsinπ/4 ] = 2 *√2/2[ sinα + cosα ] = sinαcosα = sinα( 1 -√2 )，sinα/cosα = 1/(1 -√2 )，tanα = -(1 + √2 )；tan(π/8) = tan[ (π/4)/2 ] = [ 1 - cos(π/4) ]/sin(π/4) = ( 1 -√2/2 )/(√2/2) =√2 - 1；tan(α+π/8) = [ tanα +tan(π/8) ]/[ 1 -tanαtan(π/8) ]= [ -1 -√2 +√2 - 1 ]/[ 1 + (1 + √2 )(√2 - 1) ]= -2/[ 1 + 2 - 1 ] = -1 。

1】sina=2sin(a+π/4)sina=2sinacos(π/4)+2cosasin(π/4)sina=√2*sina+√2*cosa(1-√2)sina=√2*cosatana=√2/(1-√2)=-√2*(1+√2)=-2-√22】tan(π/8)=sin(π/4)/[1+cos(π/4)]=(1/√2)/(1+1/√2)=1/(√2+1)=√2-13】tan(a+π/8)=[tana+tan(π/8)]/[1-tanatan(π/8)]=[(-2-√2)+(√2-1)]/[1+(2+√2)(√2-1)]=-3/(1+√2)=3(1-√2)