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

To solve the inequality \( \sin^2 x + a \cos x + a^2 > 1 + \cos x \) for any \( x \in \mathbb{R} \), we will follow these steps:

### Step 1: Substitute \( x = 0 \)

First, we substitute \( x = 0 \) into the inequality:

\[
\sin^2(0) + a \cos(0) + a^2 > 1 + \cos(0)
...