To simplify the expression, we need to first rewrite it as a single fraction:

sin^a + (1 - 2sin^a) / (1 - 2cos^a)

Now, let's multiply the terms in the numerator and denominator of the second fraction by sin^a:

sin^a + (1 sin^a - 2sin^a sin^a) / (sin^a - 2sin^a * cos^a)

This simplifies to:

sin^a + (sin^a - 2sin^(a+1)) / (sin^a - 2sin^a * cos^a)

Now, we can simplify further by factoring out sin^a from the numerator:

sin^a(1 + 1 - 2sin) / (sin^a(1 - 2cos))

Which simplifies to:

sin^a(2 - 2sin) / sin^a(1 - 2cos)

Finally, we can cancel out sin^a in the numerator and denominator:

(2 - 2sin) / (1 - 2cos)

Therefore, the simplified expression is:

(2 - 2sin) / (1 - 2cos)