Question

Prove that cos A -Sin A +1 / Cos A + Sin A -1 = 1+Cos A / Sin A

Answer 1

divide numerator and denominator by cosA 
we will get (tanA+secA-1)/(tanA-secA+1), in numerator replace 1 by sec^2a-tan^2A AND LET THE DEnominator be d same. 
now uu can write sec^2a-tan^2a as (seca+tan)(sec-tana),let the denominator be d same 
take seca+tana common in the numerator. yo will get seca+tan{1-seca +tana).now u will see that denominator is also{1-seca+tana}. cancel d numerator and denominator. 
only sec+tana will be remaining =rhs