AP EAMCET · Maths · Inverse Trigonometric Functions
If \(x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)\), then \(\log \sec x=\)
- A \(2 \operatorname{cosech}^{-1}\left(\cot ^2 \frac{x}{2}-1\right)\)
- B \(2 \operatorname{cosech}^{-1}\left(\cot ^2 \frac{x}{2}+1\right)\)
- C \(2 \operatorname{coth}^{-1}\left(\operatorname{cosec}^2 \frac{x}{2}-1\right)\)
- D \(2 \operatorname{coth}^{-1}\left(\operatorname{cosec}^2 \frac{x}{2}+1\right)\)
Answer & Solution
Correct Answer
(C) \(2 \operatorname{coth}^{-1}\left(\operatorname{cosec}^2 \frac{x}{2}-1\right)\)
Step-by-step Solution
Detailed explanation
For \(\begin{aligned} x \in & \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \\ & \log \sec x=y(\text { let })\end{aligned}\)…
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