What Causes the Differences in Newton's Law on an Inclined Plane?

[AxiomOfChoice]

Suppose a box is sitting, motionless, on an inclined plane which makes an angle $\theta$ with the horizontal. If I'm not mistaken, if one writes out Newton's law in the $y$ direction (if $+y$ is up), one gets $N \cos \theta - mg = 0$; i.e., $N = mg \sec \theta$. However, if you ROTATE the coordinate system so that the $x$ axis points along the incline, you get that $N = mg \cos \theta$, which is apparently RIGHT. What's going on here? Why are these two cases different?

 

[issacnewton]

hi

if the box is sitting on an incline plane and motionless, there MUST be a frictional force
which is keeping it steady. i think you are ignoring that. first draw full free body diagram and
things will become clearer.