tan(π/4+x)/tan(π/4-x)={(1+tanx)/(1-tanx)}²
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L.H.S= tan(π/4+x)/tan(π/4-x)
= tan(45+x)/tan(45-x) ∵ tan45=1 & tan(A+B)=(tanA + tanB)/1 - tanA.tanB
=((tan45 + tanx)/1-tan45.tanx)/((tan45-tanx)/1+tan45.tanx)
= (1+tanx/1-tanx)/(1-tanx/1+tanx) ∵ X/Y= X*1/Y
=(1+tanx/1-tanx)*(1+tanx/1-tanx)
={(1+tanx)/(1-tanx)}²
= R.H.S Proved.
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