1.

`(tan(pi/4+x))/(tan(pi/4-x)) = ((1+tanx)/(1-tanx))^(2)`

Answer» LHS, `therefore tan(pi/4+x) = (tanpi/4+tanx)/(1-tanpi/4.tanx)`
`therefore tan(pi/4+x) = (1+tanx)/(1-tanx)`………….(1)
Similarly, `tan(pi/4-x) = (1-tanx)/(1+tanx)`………..(2)
Divide equation (1) by equation (2),
`therefore (tan(pi/4+x))/(tan(pi/4-x)) = ((1+tanx)/(1-tanx))/((1-tanx)/(1+tanx))`
`=(1+tanx)/(1-tanx) xx (1+tanx)/(1-tanx)`
`=(1+tanx)/(1-tanx)^(2)`= RHS Hence Proved.


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