If you want to achieve better balance in tango, you can do any of the most basic leg strengthening exercises, but there are two I find focus on stability and good balance: squats and lunges. I suggest you begin with bodyweight squats. Once you get comfortable doing ten of these daily, add forward lunges. Both exercises will help your balance. (See below for links on how to do these exercises properly.)
Your balance is a combination of three systems: your vestibular system (sense of stability and spatial awareness), your vision (sight), and your proprioception (sense through which you perceive the position and movement of your body). Improving your balance requires different and complementary workouts that are specific for each of these systems. Squats and lunges target all of these systems simultaneously which is why they are a good start.
Some tips: start doing these exercises using comfortable shoes. When you get good at them and are more stable, do them in bare feet. The final challenge is to do them while wearing dance shoes. This progression will give you a wider range of foot support.
For more detail on how to do squats and lunges, you can check the two videos below. They give you good basic instructional resources:
The information in this article is not medical advice, and should not be treated as such. You must not rely on the information in this article as an alternative to medical advice from your doctor or other professional healthcare provider. If you think you may be suffering from any medical condition you should seek immediate medical attention.