A) \[2\pi \]
B) \[\frac{2\pi }{5}\]
C) \[10\pi \]
D) \[5\pi \]
Correct Answer: C
Solution :
Given, \[f(x)=\sin \left( \sin \frac{x}{5} \right)\] \[\therefore \] \[f(x+10\pi )=\sin \left[ \sin \left( \frac{x+10\pi }{5} \right) \right]\] \[=\sin \left[ \sin \left( \frac{x}{5}+2\pi \right) \right]\] \[=\sin \left( \sin \frac{x}{5} \right)=f(x)\] Hence, period of \[f(x)\]is \[10\pi \]
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