The equation `3cosx+4sinx=6` has ...... solution. finite (b) infinite (c) one (d) no

Explanation

To solve the equation \(3 \cos x + 4 \sin x = 6\), we will analyze the left-hand side and see if it can equal the right-hand side.

### Step 1: Understand the range of the left-hand side
The expression \(3 \cos x + 4 \sin x\) can be rewritten in the form \(R \sin(x + \phi)\) or \(R \cos(x + \theta)\) using the amplitude and phase shift method.

### Step 2: Calculate the amplitude \(R\)
To find \(R\), we use the formula:
\[
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