Question

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Answer 1

$\sin {}^{4} (x) - \cos {}^{4} (x) - \sin {}^{2} (x) + \cos {}^{2} (x) = \\ = - ( \cos {}^{4} (x) - \sin {}^{4} (x) ) + \cos(2x) = \\ = - ( \cos {}^{2} (x) - \sin {}^{2} (x) )( \cos {}^{2} (x) + \sin {}^{2} (x) )+ \cos(2x) = \\ = - \cos(2x) \times 1 + \cos(2x) = 0$