A) \[2\pi \]
B) \[10\pi \]
C) \[8\pi \]
D) \[5\pi \]
Correct Answer: B
Solution :
Period of \[\sin x=2\pi \] \[\Rightarrow \] period of \[{{\sin }^{3}}x=2\pi \] period of \[\left| {{\sin }^{3}}x \right|=\pi \Rightarrow \] period of \[\left| {{\sin }^{3}}\frac{x}{2} \right|=2\pi \] period of \[{{\cos }^{5}}x=2\pi \Rightarrow \] period of \[\left| {{\cos }^{5}}x \right|=\pi \] \[\Rightarrow \] period of\[\left| {{\cos }^{5}}\frac{x}{5} \right|=5\pi \] Thus required period = LCM of \[2n\] & \[5\pi =10\pi \]
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