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Range of f(x) =1/(1-2cosx) is(i)[ 1/ 3 ,...

Range of `f(x) =1/(1-2cosx)` is(i)[ 1/ 3 , 1 ] (ii) `[-1,(1)/(3)]` (iii) `(-oo,-1)uu[(1)/(3),oo)` (iv) `[-(1)/(3),1]`

A

`[(1)/(3),1]`

B

`[-1,(1)/(3)]`

C

`(-oo,-1)uu[(1)/(3),oo)`

D

`[-(1)/(3),1]`

Text Solution

Verified by Experts

The correct Answer is:
B
We known that , `-1le-cosxle1`
`rArr-2le-2cosxle2`
`rArr 1-2le1-2cos le 1+2`
`rArr -1le1-2cos xle3`
`rArr-1le(1)/(1-2cosx)le(1)/(3)`
`rArr-1lef(x)le(1)/(3)`
`:.` Range of `f=[-1,(1)/(3)]`
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