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Prove that (tan(pi/4+x))/(tan(pi/4-x))=(...

Prove that `(tan(pi/4+x))/(tan(pi/4-x))=((1+t a n x)/(1-t a n x))^2`

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It is known that `tan(A+B)=(tanA+tanB​ )/(1−tanAtanB)`
and `tan(A−B)=(tanA−tanB​)/(1+tanAtanB)`
L.H.S.=`(tan(pi/4+x))/(tan(pi/4-x))`
=`((tanπ/4+tanx)/(1-tanπ/4​tanx))/((tanπ/4​-tanx)/( (1+tanπ/4​tanx​))`
=`((1+tanx)/(1−tanx​))/((1−tanx)/(1+tanx​)​)`
=`((1+tanx)/(1-tanx​))^2`
...
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