Prove that (sin A - cos A + 1)/(sin A + cos A - 1) =cos A/1-sin ATHIS QUESTION IS FROM CHAPTER TRIGNOMETRIC IDENTITIES AND IN THIS QUESTION WE HAVE...

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)