Question

proove that (sin A-cos A+1)/(sin A+cos A-1)=1/(sec A-tan A)

Answer 1

LS= Sin A - CosA +1 / Sin A + Cos A -1 divide Numerator and Denominator by Cos A = Tan A - 1 + Sec A / Tan A + 1 - Sec A since (1+ Tan^2 A) = Sec^2 A or 1 = Sec^2 A - Tan^2 A =( Tan A + Sec A - 1) / [Tan A - Sec A+( Sec^2 A - Tan^2 A)] =( Tan A + Sec A - 1) / [(Tan A - Sec A)+( Sec^2 A - Tan^2 A)] = ( Tan A + Sec A - 1) / [- ( Sec A - tan A) + ( Sec^2 A - Tan^2 A)] = ( Tan A + Sec A - 1) / [ ( Sec A - tan A){ Tan A + Sec A - 1] = 1/ {sec A - Tan A} = RS..proved