The correct option is A order 1, degree 1
Given equation is
sinx(dx+dy)=cosx(dx−dy)
⇒sinx dx+sinx dy=cosx dx−cosx dy
⇒dx(sinx−cosx)=dy(−cosx−sinx)
⇒dydx=−sinx−cosxsinx+cosx
Hence, order and degree of the given differential equation is 1,1 respectively.