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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

(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

[Replacing 1 with ]

[Cancelling (1-SecA + TanA) in numerator and denominator]

[Multiplying numerator and denominator by (1-SinA)]