What is 2 \sin 2\alpha+\cos 2\alpha equal to?
Consider the following for the two (02) items that follow : Let 2 \sin \alpha+\cos \alpha=2 where 0 \lt \alpha \lt 90^{\circ}.
- A. 11/10
- B. 11/5 ✓
- C. 12/5
- D. 13/5
Correct Answer: B. 11/5
Explanation
Using \sin \alpha = 3/5 and \cos \alpha = 4/5, we find \sin 2\alpha = 2(3/5)(4/5) = 24/25 and \cos 2\alpha = 16/25 - 9/25 = 7/25. Therefore, 2(24/25) + 7/25 = 55/25 = 11/5.