Find the maximum and minimum values of the following expressions. (i) `3costheta+5sin(theta-pi/6)` (ii) `4sintheta-3costheta+7`

Explanation

To find the maximum and minimum values of the given expressions, we will use the properties of trigonometric functions and the concept of combining sine and cosine functions.

### (i) Expression: \( 3\cos\theta + 5\sin\left(\theta - \frac{\pi}{6}\right) \)

**Step 1:** Rewrite the expression using the sine subtraction formula.
\[ \sin\left(\theta - \frac{\pi}{6}\right) = \sin\theta \cos\frac{\pi}{6} - \cos\theta \sin\frac{\pi}{6} \]
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