I have a fraction which contains a great number of terms in numerator and denominator with cosine and sine functions along with other algebraic terms. Now as it seems to me apparently there is a common factor like (cos[eta] - sin[eta] ) or (cos[eta] + sin[eta] ) or its squared or (cos[eta]^2 - sin[eta]^2 ) in both denominator and numerator and I want to extract that common factor to bring it in a simplified form. Please throw a light on this how can I do it efficiently. Please find the attached notebook in rar file (since the size of notebook file is greater than 20 Mb). To open the attached file you have to rename the file with extension ".rar" (means rename the file with "Rdot_expr1.nb.rar" and then extract). Since I was not able to upload the .rar file hence I had to take that move. Please bear with me.

Many thanks in advance