AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(x=\log _e\left[\cot \left(\frac{\pi}{4}+\theta\right)\right]\) and \(\theta \in\left(\frac{-\pi}{4}, \frac{\pi}{4}\right)\), then consider the following statements
I. \(\cosh x=\sec 2 \theta\)
II. \(\sinh x=-\tan 2 \theta\)
- A I is true and II is false
- B I is false and II is true
- C Both I and II are true
- D Both I and II are false
Answer & Solution
Correct Answer
(C) Both I and II are true
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { We have, } x=\log \left[\cot \left(\frac{\pi}{4}+\theta\right)\right] \\ & \cosh x=\frac{e^x+e^{-x}}{2} \\ & =\frac{e^{\log \left[\cot \left(\frac{\pi}{4}+\theta\right)\right]}+e^{-\log \left[\cot \left(\frac{\pi}{4}+\theta\right)\right]}}{2} \\ &…
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