Prove that: `sin 780^0sin 480^0+cos 120^0sin 150^0=1/2`

Explanation

To prove that \( \sin 780^\circ \sin 480^\circ + \cos 120^\circ \sin 150^\circ = \frac{1}{2} \), we will simplify each term step by step.

### Step 1: Simplify \( \sin 780^\circ \)
We can reduce \( 780^\circ \) by subtracting \( 720^\circ \) (which is \( 2 \times 360^\circ \)):
\[ \sin 780^\circ = \sin(780^\circ - 720^\circ) = \sin 60^\circ \]
Using the known value:
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