Your notation is VERY confusing. Lower case letters, generally speaking, refer to the measure of the sides of a triangle, while upper case letters are generally reserved for the measures of the angles. But taking the cosine function of the measure of a side of the triangle doesn't make any sense. Hence, unless you have referred to BOTH the measure of a side of the triangle and a measure of an angle with the same variable (sort of like calling everyone in the room "George" regardless of what their names really are), you must be saying that the ratio of the measure of one of the angles to the cosine of the measure of the other acute angle is equal to the ratio of the measure of the other acute angle to the cosine of the measure of the first angle -- an assertion that is false for all except an isosceles right triangle.
