Find the maximum value of `4sin^2x+3cos^2x+sinx/2+cosx/2dot`

Explanation

To find the maximum value of the expression \( 4\sin^2 x + 3\cos^2 x + \frac{\sin x}{2} + \frac{\cos x}{2} \), we can follow these steps:

### Step 1: Rewrite the expression
We can rewrite \( \cos^2 x \) in terms of \( \sin^2 x \):
\[ \cos^2 x = 1 - \sin^2 x \]
Thus, the expression becomes:
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