I been working on this forever. I am stuck at the integration part.

the problem is:

cosysint dy/dt = sinycost

the answer is

y=arcsin(C sint)

Here is my attempt :

cosy/siny dy = cost/sint dt

arctany dy = arctant dt

then i integrate both side and get

yarctany-1/2ln(1+y^2)=tarctant-1/2ln(1+t^2)

some there i am stuck.. i dunno how to get the answer y=arcsin(c sint)