What is \tan \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. 1/2
- B. 1
- C. 3/4 ✓
- D. 2
Correct Answer: C. 3/4
Explanation
Given \cos \alpha = 2 - 2\sin \alpha. Squaring gives 1-\sin^2 \alpha = 4(1-\sin \alpha)^2. Since 0 \lt \alpha \lt 90^{\circ}, \sin \alpha \neq 1. Dividing by 1-\sin \alpha yields 1+\sin \alpha = 4 - 4\sin \alpha \implies 5\sin \alpha = 3. Hence \sin \alpha = 3/5 and \cos \alpha = 4/5, so \tan \alpha = 3/4.