I input the following into the web-based Mathematica and it timed out
before giving an answer. Can anyone help finding out if there is a
symbolic answer:

sin[x]*sqrt(1-a*(cos[x])^2*((1+sin[x])^2/(1+a*sin[x])^2+(1-
a)*cos[x]^2))

Please copy and paste the formula in order to avoid introducing
errors. Thank you.