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The period of f(x)=(1)/(2){(| sinx|)/...

The period of
`f(x)=(1)/(2){(| sinx|)/(cos x)+(|cos|)/(sinx)}`, is

A

`2pi`

B

`pi`

C

`(pi)/(2)`

D

`(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
We observe that `(|sinx|)/(cosx) and (|cosx|)/(sinx)` are periodic functions each with period `2pi` . Also, there is no positive real number T between 0 and `2pi` such that `f(x+T)=f(x)` .
So, f(x) is periodic with period `2pi` .
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OBJECTIVE RD SHARMA-REAL FUNCTIONS -Chapter Test
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  13. If f(x) is defined on [0,1], then the domain of f(3x^(2)) , is

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  14. The function f(x) is defined in [0,1] . Find the domain of f(t a nx)do...

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  15. The domain of definition of the real function f(x)=sqrt(log(12)x^(2)) ...

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  21. If x in R , then f(x)=cos^(-1)((1-x^(2))/(1+x^(2))) is equal to

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