If \sec^{-1}p-\operatorname{cosec}^{-1}q=0 where p \gt 0, q \gt 0; then what is the value of p^{-2}+q^{-2}?
- A. 1 ✓
- B. 2
- C. \frac{1}{2}
- D. \frac{1}{2\sqrt{2}}
Correct Answer: A. 1
Explanation
Let \sec^{-1}p = \operatorname{cosec}^{-1}q = \theta. This means p = \sec\theta and q = \operatorname{cosec}\theta. The expression becomes p^{-2} + q^{-2} = \frac{1}{\sec^2\theta} + \frac{1}{\operatorname{cosec}^2\theta} = \cos^2\theta + \sin^2\theta = 1.