tan派/8-tan3派/8

tan(π/8)-tan(3π/8)
=sin(π/8)/cos(π/8)-sin(3π/8)/cos(3π/8)
=[sin(π/8)cos(3π/8)-cos(π/8)sin(3π/8)]/[cos(π/8)cos(3π/8)]
=sin(π/8-3π/8)/{[cos(π/8+3π/8)+cos(π/8-3π/8)]/2}
=2sin(-π/4)/[cos(π/2)+cos(-π/4)]
=-2sin(π/4)/[0+cos(π/4)]
=-2•(√2/2)/(√2/2)
=-2

先化弦,再用两角和和积化和差公式转化为特殊角就可以了.当然也可以用半角公式来做