If x-rays and mammograms can cause cancer, then why do them annually as a checkup procedure? if they cause harm, why drs recommend them??

There's good and bad: "Everything" causes cancer. If the benefit of finding a cancer tumor early outweighs the tiny risk from an x-ray, it's ok to do. To reduce your cancer risk, keep a healthy weight and exercise (at least 30 minutes, 5 days a week). Eat lots vegetables and limit your intake of red meat or burned/charbroiled meat. Avoid smoking, which increases risk of lung cancer, oral and throat cancers, etc...