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`

If we put, `x = 0`, equation becomes,

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

`=>a+a^2 gt 2`

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

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

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

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

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