Solve the given differential equation by separation of varia

Solve the given differential equation by separation of variables. csc y dx + (sec^2) x dy = 0

cscy*dx + sec^2x*dy = 0

cscy*dx = -sec^2x*dy

dy/cscy = -dx/sec^2x

siny*dy = -cos^2x*dx

Integrating :

-cos(y) = (integral) (cos(2x) - 1)/2 * dx

-cos(y) = -x/2 - sinxcosx/2 + D

Negating all over :

cos(y) = x/2 + sinxcosx/2 + C

y = arccos(x/2 + sinxcosx/2 + C) ---> ANSWER