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If tanA=m/(m-1)\ and tanB=1/(2m-1), then...

If `tanA=m/(m-1)\ and tanB=1/(2m-1),` then prove that `A-B=\ pi/4`

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Given `tan A = (m)/(m−1);tan B = 1/(2m−1)`
We know that `tan (A - B) = (tanA−tanB)/(1+tanAtanB)`
`=((m)/(m−1)-1/(2m−1))/(1-(m)/(m−1)1/(2m−1))`
`=(2m^2-m-m-1)/(2m^2-m-2m+1+m)`
`=(2m^2-2m+1)/((2m^2-2m+1)`
`=1`
`A-B=tan^(-1)(1)`
`=(pi)/4`
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