Question

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: $\sinh \, x = - \tan \, 2 \theta$
Then which one of the following options is true?

• 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 1

Answer: (C)

Correct answer is (c) Both I and II are true