1 - cosa + cos2a / sin2a - sina = ctga

To simplify this expression, we first look for common terms that can be factored out:

cos2a can be written as 2cos^2(a) - 1

1 - cosa + 2cos^2(a) - 1 / sin2a - sina

Now, we can simplify further:

2cos^2(a) - cosa / sin2a - sina

Next, we can factor out a cos(a) from the numerator and a sin(a) from the denominator:

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

Now, we can cancel out the common term in the numerator and denominator:

cos(a) / sin(a) = ctga

Therefore, the expression simplifies to ctga.