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2014-08-04T23:34:59+05:30

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Multiply numerator and denominator by cos A

(1 + sin A  - cosA) / (sin A + cos A -1 )
multiply numerator and denominator by (sinA + cos A +1)

(1+sinA - cos A) (1+sinA+cosA)  / [ (sinA+ cosA) - 1 ] [ (sin A+cosA)+1]
[ (1+sin A)² - cos² A ] / [ (sinA+ cosA)² - 1² ]
[ 1 + sin²A + 2 sinA - cos²A ]  / [ sin²A+cos²A+2sinA cosA - 1 ]
= [ 2 sin² A + 2 sin A ]  /  2 sin A cos A
= 2 sin A [sin A + 1 ] / 2 sin A cos A
= (1 + sin A )/ cos A 
multiply by 1 - sine A in numerator , denomninator
= (1- sine ² A) / cos A  (1-sinA)
= cos²A / cosA (1-sinA)
cosA/1-sin A
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2014-08-05T11:25:58+05:30
Consider LHS
\frac{secA+tanA -1}{tan A -secA +1}

\frac{(SecA+TanA) -(Sec^2A - Tan^2A)}{tan A -secA +1} [Replacing 1 with Sec^2A - Tan^2A]

\frac{(SecA+TanA)(1-SecA + TanA)}{tan A -secA +1} [Cancelling (1-SecA + TanA) in numerator and denominator]

SecA+TanA   

 \frac{1}{CosA} +  \frac{SinA}{CosA}

 \frac{1+SinA}{CosA}

 \frac{(1+SinA)(1-SinA)}{(CosA)(1-SinA)}    [Multiplying numerator and denominator by (1-SinA)]

 \frac{(1-Sin^2A)}{(CosA)(1-SinA)} 

\frac{(Cos^2A)}{(CosA)(1-SinA)}

 \frac{CosA}{1-SinA}

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