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