First of all, to lose belly fat, you have to do mild to moderate cardio. Depending on your injury, if you have sciatica or if makes your feet hurt, walking may or may not be a good, low impact way to lose fat, otherwise swimming may be pain free or using ellipticals and other machines like it. I like to use ellipticals because there's no impact on the back or feet.
Not sure what your injury is, but I too have had back and neck injuries and core strengthening exercises made it better.
Don't do anything that hurts and use proper technique - always keep your head and neck neutral and in allignment with your spine.
Planks are super important for the main abdominal muscle and shouldn't hurt you.
Do crunches and side crunches to work the six pack muscle.
Side Planks are important for strengthening the lower back muscles, important for a strong core.
Superman's are important for strengthening the muscles along your spine, which will help ease any back pain.
To help heal your back and neck, I'd advise doing some stretches too! Some yoga postures and physio stretches have been amazing for me, along with doing planks often.
Child's pose, The cat/cow stretch, and the Cobra stretch are the 3 main stretches that have eliminated my back and neck pain.
Also, good flexibility improves your overall fat loss and muscle strength.
If you haven't tried Self Deep Tissue Massage or Trigger Point Therapy, I highly reccomend it, as it's easy to do yourself.
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