What is \tan^2 \alpha 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. 8 ✓
- B. 6
- C. 4
- D. 3
Correct Answer: A. 8
Explanation
From the given, \sin^2 \beta = \frac{9}{32}\sin^2 \alpha and \cos^2 \beta = \frac{81}{12}\cos^2 \alpha = \frac{27}{4}\cos^2 \alpha. Since \sin^2 \beta + \cos^2 \beta = 1, we get \frac{9}{32}\sin^2 \alpha + \frac{27}{4}\cos^2 \alpha = 1. Dividing by \cos^2 \alpha and using \sec^2 \alpha = 1+\tan^2 \alpha gives \tan^2 \alpha = 8.
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