Question

$\cos {}^{4} ( \alpha ) - \sin {}^{4} ( \alpha )$


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Answer 1

$\cos {}^{4} ( \alpha ) - \sin {}^{4} ( \alpha )$

Answer is in attachment

Answer 2

$heya \\ \\ \\ \\ \ \cos {}^{4} ( \alpha ) - \sin {}^{4} ( \alpha ) = \\ \\ \\ ( \cos {}^{2} ( \alpha ) + \sin {}^{2} ( \alpha ) ) \times ( \cos {}^{2} ( \alpha ) - \sin {}^{2} ( \alpha ) ) \\ \\ \\ \\ (1) \times ( \cos {}^{2} ( \alpha ) - 1 + \cos {}^{2} ( \alpha ) ) \\ \\ \\ 2 \cos {}^{2} ( \alpha ) - 1 \\ \\ = \cos(2 \alpha )$