If `cos^2x-(c-1)cosx+2cgeq6` for every `x in R ,` then the true set of values of `c` is `(2,oo)` (b) `(4,oo)` (c) `(-oo,-2)` (d) `(-oo,-4)`

Explanation

To solve the inequality \( \cos^2 x - (c - 1) \cos x + 2c \geq 6 \) for every \( x \in \mathbb{R} \), we can follow these steps:

### Step 1: Rearranging the Inequality
We start by rearranging the inequality:
\[ \cos^2 x - (c - 1) \cos x + 2c - 6 \geq 0 \]
This simplifies to:
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