Prove that sin 10° + sin 20° + sin 40° + sin 50°=sin 70° + sin 80

Explanation

To prove that \( \sin 10^\circ + \sin 20^\circ + \sin 40^\circ + \sin 50^\circ = \sin 70^\circ + \sin 80^\circ \), we will start with the left-hand side (LHS) and manipulate it to show that it is equal to the right-hand side (RHS).

### Step 1: Write down the LHS
We start with the left-hand side:
\[ \text{LHS} = \sin 10^\circ + \sin 20^\circ + \sin 40^\circ + \sin 50^\circ \]

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