Proving that: (sin x + cos x)² + (sin x - cos x)² = 2
Work.
(sin x + cos x)² + (sin x - cos x)² = 2
Distribute.
(sin²x + 2 sin x cos x + cos²x ) + (sin²x - 2 sin x cos x + cos²x) = 2
Combine like terms.
sin²x + cos²x + sin²x + cos²x = 2
Pythagorean identity where sin²x + cos²x = 1.
1 + 1 = 2
2 = 2
Thus, (sin x + cos x)² + (sin x - cos x)² = 2
