What is (sin 9° – cos 9°) equal to?

(sin9° – cos9°)² = sin²9° + cos²9° – 2sin9°cos9° = 1 – sin18° = 1 – (√5–1)/4 = (5 – √5)/4. So |sin9° – cos9°| = √(5–√5)/2. Since cos9° > sin9° (as 9° < 45°), sin9° – cos9° < 0. Therefore sin9° – cos9° = –√(5–√5)/2.