If ` sin alpha =(1)/(2) ,` prove that `(3 cos alpha - 4 cos ^(3) alpha )=0.`

Explanation

To prove that \(3 \cos \alpha - 4 \cos^3 \alpha = 0\) given that \(\sin \alpha = \frac{1}{2}\), we can follow these steps:

### Step 1: Find \(\cos \alpha\)
Since we know \(\sin \alpha = \frac{1}{2}\), we can use the Pythagorean identity:
\[ \sin^2 \alpha + \cos^2 \alpha = 1. \]
Substituting the value of \(\sin \alpha\):
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