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 (a) -4 (b) -3 (c) `-2` (d) `-1`

Options

A. `-4`
B. `-3`
C. `-2`
D. `-1`

Answer

B

Explanation

`sin^(2) x+a cos x + a^(@) gt 1+ cos x`
Putting `x=0`, we get
or `a+a^(2) gt 2`
or `a^(2) +a-2 gt 0`
or `(a+2) (a-1) gt 0`
or `a lt -2 or a gt 1`
Therefore, we have the largest negative integral value of `a=-3`.