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`

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: Rewrite the inequality
We start with the given inequality:
\[ \sin^2 x + a \cos x + a^2 > 1 + \cos x \]
Using the identity \( \sin^2 x + \cos^2 x = 1 \), we can express \( \sin^2 x \) as \( 1 - \cos^2 x \):
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