If the inequality `sin^2x+acosx+a^2>1+cosx` holds for any `x in R ,` then the largest negative integral value of a is `-4` (b) -3 (c) `-2` (d) `-1`

Explanation

`sin^2x+acosx +a^2 gt 1+cosx` for `x in R`

As `x in R`, we can put, `x = 0`

`=>(sin0)^2+acos0 +a^2 gt 1+cos0`

`=>a+a^2 gt 2`

`=>a^2+a -2 gt 0`

`=> (a+2)(a-1) gt 0`

`:. a in (-oo,-2) uu (1,oo)`

So, largest negative integral value of `a` will be `-3` as `-2` is not included.