AP EAMCET · Maths · Trigonometric Ratios & Identities
The larger of \(\cos (\log \theta)\) and \(\log (\cos \theta)\), if \(e^{-\pi / 2} < \theta < \pi / 2\) is
- A \(\cos (\log \theta)\)
- B \(\log (\cos \theta)\)
- C none of function is larger
- D one of the two function is undefined on domain even to compare
Answer & Solution
Correct Answer
(A) \(\cos (\log \theta)\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { } \cos (\log \theta), \theta \in\left(e^{\frac{-\pi}{2}}, \frac{\pi}{2}\right) \\ & e^{-\frac{\pi}{2}} < \theta < \frac{\pi}{2} \\ & \Rightarrow \quad-\frac{\pi}{2} < \log \theta < \log \frac{\pi}{2} \leq \frac{\pi}{2} \end{aligned} \] So,…
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