What is \tan^2 \beta equal to?
For the following two (02) items: Let \frac{\sin \alpha}{\sin \beta} = \frac{4\sqrt{2}}{3} and \frac{\cos \alpha}{\cos \beta} = \frac{2\sqrt{3}}{9}.
- A. 1/2
- B. 3/2
- C. 1/3 ✓
- D. 2/3
Correct Answer: C. 1/3
Explanation
Given \tan^2 \alpha = 8, we find \sin^2 \alpha = \frac{8}{9}. Substituting this into the first relation gives \sin^2 \beta = \frac{9}{32} \times \frac{8}{9} = \frac{1}{4}. Thus \cos^2 \beta = \frac{3}{4}, and \tan^2 \beta = \frac{1/4}{3/4} = \frac{1}{3}.
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