1.

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`

Answer» `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.


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