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The equality sin A+ sin 2A + sin 3A = 3 ...

The equality `sin A+ sin 2A + sin 3A = 3` holds for some real value of A.

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To determine whether the equality \( \sin A + \sin 2A + \sin 3A = 3 \) holds for some real value of \( A \), we can analyze the maximum values of the sine function. ### Step-by-Step Solution: 1. **Understanding the Sine Function**: The sine function, \( \sin x \), has a maximum value of 1 for any angle \( x \). Therefore, for the expression \( \sin A + \sin 2A + \sin 3A \) to equal 3, each term must reach its maximum value simultaneously. 2. **Setting Up the Equation**: ...
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