If `sin^2(theta-alpha)c a salpha=cos^2(theta-alpha)sinalpha=msinalphacosalpha,` then prove that `|m|geq1/(sqrt(2))`

Explanation

To prove that \( |m| \geq \frac{1}{\sqrt{2}} \) given the equations \( \sin^2(\theta - \alpha) \cos \alpha = m \sin \alpha \cos \alpha \) and \( \cos^2(\theta - \alpha) \sin \alpha = m \sin \alpha \cos \alpha \), we can follow these steps:

### Step 1: Set up the equations
From the first equation, we have:
\[ \sin^2(\theta - \alpha) \cos \alpha = m \sin \alpha \cos \alpha \]
Assuming \( \cos \alpha \neq 0 \), we can divide both sides by \( \cos \alpha \):
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