Prove that:
`cos(pi/10)-sin(pi/10)=sqrt(2)sin((3pi)/(20))`

Explanation

To prove that \( \cos\left(\frac{\pi}{10}\right) - \sin\left(\frac{\pi}{10}\right) = \sqrt{2} \sin\left(\frac{3\pi}{20}\right) \), we will start with the left-hand side and manipulate it to reach the right-hand side.

### Step 1: Rewrite the cosine term
We can use the identity \( \cos\left(\theta\right) = \sin\left(\frac{\pi}{2} - \theta\right) \) to rewrite \( \cos\left(\frac{\pi}{10}\right) \):
\[ \cos\left(\frac{\pi}{10}\right) = \sin\left(\frac{\pi}{2} - \frac{\pi}{10}\right) = \sin\left(\frac{5\pi}{10} - \frac{\pi}{10}\right) = \sin\left(\frac{4\pi}{10}\right) \]
Thus, we can express the left-hand side as:
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