Trigonometrical confusion!

Geometry Level 2

If \(\alpha\) + \(\beta\) = \(\large\frac{\pi}{2}\) and \(2\)[\(cos^{2}\)\(\alpha\) \(-\)\(cos^{2}\)\(\beta\)] = \(1\) , then find the value of \(\alpha\).

Assume \( 0\leq \alpha \leq\frac\pi2\).

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