If `cos^2x-(c-1)cosx+2cgeq6` for every `x in R ,` then the true set of values of `c` is (a) `(2,oo)` (b) `(4,oo)` (c) `(-oo,-2)` (d) `(-oo,-4)`

Explanation

`cos^2x-(c-1)x + 2c ge 6`

`=>cos^2x-(c-1)cosx+2c-6 ge 0`

`=>cos^2x-(c-3)cosx - 2cosx+(2c-6) ge 0`

`=>cosx(cosx-(c-3))-2(cosx-(c-3)) ge 0`

`=>(cosx-(c-3))(cosx-2) ge 0`

As, `cosx - 2` can not be greater than or equal to `2`.

`:. cosx le c-3`

`=>1 le c-3`

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