NDA 2024 · PYQ · Trigonometry · medium
What is (sin 9° – cos 9°) equal to?
Answer
The correct answer is A: –√(5 – √5)/2. (sin9° – cos9°)² = sin²9° + cos²9° – 2sin9°cos9° = 1 – sin18° = 1 – (√5–1)/4 = (5 – √5)/4. So |sin9° – cos9°| = √(5–√5)/2.
- A.–√(5 – √5)/2✓ Correct
- B.–√(5 – √3)/2
- C.√(5 – √5)/2
- D.√(5 – √5)/4
(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.
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