What is a value of (\operatorname{cosec} \theta + \sec \theta) ?
For the next two (02) items that follow : Let 12(\tan \theta + \cot \theta) = 25, where 45^\circ < \theta < 90^\circ.
- A. 4
- B. \frac{35}{12} ✓
- C. \frac{25}{12}
- D. 2
Correct Answer: B. \frac{35}{12}
Explanation
From the previous evaluation, \sin \theta = \frac{4}{5} and \cos \theta = \frac{3}{5}. Therefore, \operatorname{cosec} \theta = \frac{5}{4} and \sec \theta = \frac{5}{3}. Their sum is \frac{5}{4} + \frac{5}{3} = \frac{15+20}{12} = \frac{35}{12}.
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