Prove that cos 2A = 1 − 2sin²A.

cos 2A = cos²A − sin²A = (1 − sin²A) − sin²A = 1 − 2sin²A.

No citable source has been recorded for this record. Treat it as practice material, not as fact.

Explanation

The same identity in the other direction gives sin²A = (1 − cos 2A)/2, which is used constantly in integration.