The equation `3cosx+4sinx=6` has ...... solution.

Options

A. Finite
B. Infinite
C. Unique or one solution
D. No solution

Explanation

To solve the equation \(3 \cos x + 4 \sin x = 6\), we will analyze the possible values of the left-hand side expression.

### Step 1: Determine the range of \(3 \cos x + 4 \sin x\)

We know that for any linear combination of sine and cosine, such as \(A \cos x + B \sin x\), the maximum and minimum values can be determined using the formula:

\[
\sqrt{A^2 + B^2}
...