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Maths-

General

Easy

Question

The period of the function $open vertical bar sin cubed space x over 2 close vertical bar plus open vertical bar cos to the power of 5 space x over 5 close vertical bar$ is

$2 π$
$10 π$
$8 π$
$5 π$

hint Hint:

In this question, we have to find the period of $open vertical bar sin cubed space x over 2 close vertical bar plus open vertical bar cos to the power of 5 space x over 5 close vertical bar$ . Firstly, we will find the period of trigonometric functions and later find the period of function i.e., 1/2 of LCM of periods obtained.

The correct answer is: $10 pi$

$open vertical bar sin cubed space x over 2 close vertical bar plus open vertical bar cos to the power of 5 space x over 5 close vertical bar P e r i o d space o f space open vertical bar sin cubed space x over 2 close vertical bar space i s space 4 straight pi Period space of space open vertical bar cos to the power of 5 space straight x over 5 close vertical bar space is space 10 straight pi Therefore comma space period space of space open vertical bar sin cubed space straight x over 2 close vertical bar plus open vertical bar cos to the power of 5 space straight x over 5 close vertical bar equals 1 half cross times LCM space of space 4 straight pi space and space 10 straight pi equals 1 half cross times 20 straight pi equals 10 straight pi$

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