Prove that:

(tan(x/4 + x)) / (tan(x/4 - x)) = ((1 + tan(x)) / (1 - tan(x)))²

L.H.S = (tan(π/4 + x)) / (tan(π/4 - x))

= ((tan(π/4) + tan(x)) / (1 - tan(π/4)·tan(x))) ÷ ((tan(π/4) - tan(x)) / (1 + tan(π/4)tan(x)))

= ((1 + tan(x)) / (1 - tan(x))) ÷ ((1 - tan(x)) / (1 + tan(x)))

= ((1 + tan(x)) / (1 - tan(x)))²

= R.H.S