What is \sec \theta equal to?
For the following two (02) items: Let \frac{1+\sin \theta}{\cos \theta} = p + \sqrt{p^2+1}.
- A. p
- B. \sqrt{p^2 + 1} ✓
- C. \frac{1}{\sqrt{p^2 + 1}}
- D. \frac{p}{\sqrt{p^2 + 1}}
Correct Answer: B. \sqrt{p^2 + 1}
Explanation
We have \sec \theta + \tan \theta = \sqrt{p^2+1} + p. Taking the reciprocal gives \sec \theta - \tan \theta = \sqrt{p^2+1} - p. Adding these two equations yields 2\sec \theta = 2\sqrt{p^2+1}, so \sec \theta = \sqrt{p^2+1}.
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