A) \[\left[ -\pi ,\pi \right]\]
B) \[\left[ -1,1 \right]\]
C) \[\left[ 0,1 \right]\]
D) \[\left[ -1,0 \right]\]
Correct Answer: B
Solution :
| We have, \[y=\cos \left( \pi \sin \left( \frac{\pi }{2}\cos \left( \pi \sin x \right) \right) \right)\] |
| \[-1\le \sin x\le 1\] |
| \[\therefore \,\,\,\,-\pi \le \sin x\le \pi \] \[\Rightarrow -1\le \cos (\pi \sin x)\le 1\] \[\Rightarrow -1\le \sin \left( \frac{\pi }{2}\cos \left( \pi \sin x \right) \right)\le 1\] \[\Rightarrow -\pi \le \pi \sin \left( \frac{\pi }{2}\cos \left( \pi \sin x \right) \right)\le \pi \] |
| \[\Rightarrow -1\le \cos \left( \pi \sin \left( \frac{\pi }{2}\cos \left( \pi \sin x \right) \right) \right)\le 1\] \[\Rightarrow -1\le y\le 1\] Range of \[y\in \left[ -1,1 \right]\] |
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