We have to prove that (sin A - cos A + 1)/(sin A + cos A - 1) = cos A/(1 - sin A)

Start from the left hand side

(sin A - cos A + 1)/(sin A + cos A - 1)

=> (sin A - cos A +...

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We have to prove that (sin A - cos A + 1)/(sin A + cos A - 1) = cos A/(1 - sin A)

Start from the left hand side

(sin A - cos A + 1)/(sin A + cos A - 1)

=> (sin A - cos A + 1)(sin A - cos A -1)/(sin A + cos A - 1)(sin A - cos A -1)

=> ((sin A - cos A)^2 - 1)/((sin A - 1)^2 - (cos A)^2)

=> ((sin A - cos A)^2 - 1)/((sin A)^2 - 2*sin A + 1 - (cos A)^2)

=> ((sin A - cos A)^2 - 1)/((sin A)^2 - 2*sin A + (sin A)^2)

=> ((sin A)^2 + (cos A)^2 - 2*sin A*cos A - 1)/((sin A)^2 - 2*sin A + (sin A)^2)

=> (1- 2*sin A*cos A - 1)/((sin A)^2 - 2*sin A + (sin A)^2)

=> (-2*sin A*cos A)/(2*(sin A)^2 - 2*sin A)

=> (-cos A)/(sin A - 1)

=> cos A/(1 - sin A)

which is the right hand side

**This proves:(sin A - cos A + 1)/(sin A + cos A - 1) = cos A/(1 - sin A)**