How would I verify the following trig equation? $$\frac{\sin(A)}{\sin(A) + \cos(A)}=\frac{\sec(A)}{\sec(A)+\cos(A)}$$
My work so far is to write the RHS as $$\frac{1/\cos(A)}{1/\cos(A) + \cos(A)}$$
But I am not sure what I can do to prove the identity.