证明:tan[3x/2]-tan[x/2]=2sinx/[cosx+cos2x]
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证明:tan[3x/2]-tan[x/2]=2sinx/[cosx+cos2x]证明:tan[3x/2]-tan[x/2]=2sinx/[cosx+cos2x]证明:tan[3x/2]-tan[x/2
证明:tan[3x/2]-tan[x/2]=2sinx/[cosx+cos2x]
证明:tan[3x/2]-tan[x/2]=2sinx/[cosx+cos2x]
证明:tan[3x/2]-tan[x/2]=2sinx/[cosx+cos2x]
tan(3x/2)-tan(x/2)
=sin(3x/2)/cos(3x/2)-sin(x/2)/cos(x/2)(通分)
=[sin(3x/2)cos(x/2)-cos(3x/2)sin(x/2)]/[cos(3x/2)cos(x/2)]
=sin(3x/2-x/2]/[(1/2)(cos2x+cosx)(积化和差)
=2sinx/(cosx+cos2x)
故原式成立.
证明:tan[3x/2]-tan[x/2]=2sinx/[cosx+cos2x]
证明:tan[3x/2]-tan[x/2]=2sinx/[cosx+cos2x]
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tan( x/2+π/4)+tan(x/2-π/4 )=2tanxtan(x/2+π/4)+tan(x/2-π/4)=[tan(x/2)+tan(π/4)]/[1-tan(x/2)tan(π/4)]+[tan(x/2)-tan(π/4)]/[1+tan(x/2)tan(π/4)]=[tan(x/2)+1]/[1-tan(x/2)]+[tan(x/2)-1]/[1+tan(x/2)]=[(tan(x/2)+1)^2-(tan(x/2)-1)^2]/[1-(tan(x