Prove the following identity: `4(cos^3 10^0+sin^3\ \ 20^0)=\ 3\ (cos 10^0+sin 20^0)`

Explanation

To prove the identity \( 4(\cos^3 10^\circ + \sin^3 20^\circ) = 3(\cos 10^\circ + \sin 20^\circ) \), we can follow these steps:

### Step 1: Use the identity for \( \sin^3 \theta \) and \( \cos^3 \theta \)

We know the identities:
\[ \sin^3 \theta = \frac{3\sin \theta - \sin(3\theta)}{4} \]
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