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Th range of k for which the inequaliity ...

Th range of k for which the inequaliity `kcos^2x-kcosx+1>=0 AA x in(-oo,oo) is`

A

`klt- 1/2`

B

`kgt4`

C

`-1/2lekle4`

D

`1/2lekle5`

Text Solution

Verified by Experts

The correct Answer is:
C
`kcos^2x-kcos+1le0AAx in(-oo,oo)`
`rArrk(cos^2x-cosx)+1ge0`
But `cos^2x-cosx=(cosx-1/2)^2-1/4`
`rArr -1/4lecos^2x-cosxle2`
Now, from (i), we get `2k+1ge0rArr kge-1/2`
Also, `-k/4+1ge0`
`rArr kle4`
`rArr -1/2lekle4`
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