The points on the curve y=sinx where the tangent lines are parallel to x− axis are given by
x=nπ,n∈z
x=2nπ,n∈z
x=(2n+1)π2,n∈z
x=(2n+1)π,n∈z
dydx=0⇒cosx=0
x=(2n+1)π2 where n∈z