CUET · MATHS · PYQ PAPER 2023
The interval in which \(f(x)=\sin x-\cos x, 0 \leq x \leq 2 \pi\) is strictly decreasing is:
- A \(\left(\frac{\pi}{4}, \frac{5 \pi}{4}\right)\)
- B \(\left(0, \frac{\pi}{4}\right) \cup\left(\frac{5 \pi}{4}, 2 \pi\right)\)
- C \(\left(\frac{3 \pi}{4}, \frac{7 \pi}{4}\right)\)
- D \(\left(0, \frac{3 \pi}{4}\right) \cup\left(\frac{7 \pi}{4}, 2 \pi\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{3 \pi}{4}, \frac{7 \pi}{4}\right)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \cos x + \sin x\) \(\cos x + \sin x \(\sqrt{2} \sin\left(x + \frac{\pi}{4}\right) \(\pi \(\frac{3\pi}{4} < x < \frac{7\pi}{4}\)
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