How can equating forces in different directions yield different results?

An object of mass m is resting on a plane inclined at angle A to the horizontal, and there is no motion. The weight (mg) of the object acts directly downwards, and the normal reaction (R) between the object and the plane acts perpendicular to the plane. Resolving vertically will yield the following result: RcosA=mg . However, I have also seen a method which equates the two forces perpendicular to the plane, thus yielding R=mgcosA . How can both of these be correct, since mgcosA is obviously not equal to mg/cosA ?