Prove that `(sin20^(@) + sin40^(@)) + (cos20^(@) + cos40^(@))=(sqrt(3)+1)cos10^(@)`

Explanation

To prove that \((\sin 20^\circ + \sin 40^\circ) + (\cos 20^\circ + \cos 40^\circ) = (\sqrt{3}+1)\cos 10^\circ\), we will use the sum-to-product identities for sine and cosine.

### Step-by-Step Solution:

1. **Write down the expression:**
\[ \sin 20^\circ + \sin 40^\circ + \cos 20^\circ + \cos 40^\circ \]
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