The period of the function `|sin^3(x/2)|+|cos^5(x/5)|` is

Options

A. `2pi`
B. `10pi`
C. `8pi`
D. `5pi`

Answer

B

Explanation

`f(x)=|"sin"^(3)(x)/(2)|+|"cos"^(5)(x)/(5)|`
The period of `sin^(3)x` is `2pi`.
So, the period of ` "sin"^(3)(x)/(2) " is " (2pi)/(1//2)=4pi.`
So, the period of `|"sin"^(3)(x)/(2)|" is " 2pi.`
The period of `cos^(5) x " is " 2pi.`
So, the period of ` "cos"^(5)(x)/(5) " is " (2pi)/(((1)/(5)))=10pi.`
So, the period of `|"cos"^(5)(x)/(2)| " is " 5pi`
So, the period of `|"cos"^(5)(x)/(2)| " is " 5pi`
Now, period of `f(x)=LCM " of " {2pi,5pi}=10pi`