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For all theta in [ 0, pi//2], show tha...

For all `theta` in `[ 0, pi//2]`, show that `cos ( sin theta) gt sin (cos theta)`.

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To prove that \( \cos(\sin \theta) > \sin(\cos \theta) \) for all \( \theta \) in the interval \( [0, \frac{\pi}{2}] \), we will follow these steps: ### Step 1: Analyze the functions involved We start by noting the behavior of the functions \( \sin \theta \) and \( \cos \theta \) in the interval \( [0, \frac{\pi}{2}] \). In this interval: - \( \sin \theta \) increases from 0 to 1. - \( \cos \theta \) decreases from 1 to 0. ### Step 2: Establish the inequality ...
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